Digital counting of individual molecules by stochastic attachment of diverse labels

ABSTRACT

Compositions, methods and kits are disclosed for high-sensitivity single molecule digital counting by the stochastic labeling of a collection of identical molecules by attachment of a diverse set of labels. Each copy of a molecule randomly chooses from a non-depleting reservoir of diverse labels. Detection may be by a variety of methods including hybridization based or sequencing. Molecules that would otherwise be identical in information content can be labeled to create a separately detectable product that is unique or approximately unique in a collection. This stochastic transformation relaxes the problem of counting molecules from one of locating and identifying identical molecules to a series of binary digital questions detecting whether preprogrammed labels are present. The methods may be used, for example, to estimate the number of separate molecules of a given type or types within a sample.

RELATED APPLICATIONS

This application is a continuation of U.S. Pat. Application No. 16/846,133, filed on Apr. 10, 2020, which is a continuation of U.S. Pat. Application No. 15/217,886, filed on Jul. 22, 2016, now U.S. Pat. No. 10,619,203, which is a continuation of U.S. Pat. Application No. 14/281,706, filed on May 19, 2014, now U.S. Pat. No. 9,816,137, which is a continuation of U.S. Pat. Application No. 12/969,581, filed on Dec. 15, 2010, now U.S. Pat. No. 8,835,358, which claims priority to U.S. Provisional Application No. 61/286,768, filed on Dec. 15, 2009. The content of each of these related applications is incorporated herein by reference herein in its entirety.

REFERENCE TO SEQUENCE LISTING

The present application is being filed along with a Sequence Listing in electronic format. The Sequence Listing is provided as a file entitled 68EB-298684-US12, created Feb. 8, 2023, which is 2,543,616 bytes in size. The information in the electronic format of the Sequence Listing is incorporated herein by reference in its entirety.

FIELD OF THE INVENTION

Methods, compositions and products for counting individual molecules by stochastic attachment of diverse labels from a set of labels, followed by amplification and detection are disclosed.

BACKGROUND OF THE INVENTION

Many processes are characterized or regulated by the absolute or relative amounts of a plurality of items. For example, in biology, the level of expression of particular genes or groups of genes or the number of copies of chromosomal regions can be used to characterize the status of a cell or tissue. Analog methods such as microarray hybridization methods and real-time PCR are alternatives, but digital readout methods such as those disclosed herein have advantages over analog methods. Methods for estimating the abundance or relative abundance of genetic material having increased accuracy of counting would be beneficial.

The availability of convenient and efficient methods for the accurate identification of genetic variation and expression patterns among large sets of genes may be applied to understanding the relationship between an organism’s genetic make-up and the state of its health or disease, Collins et al, Science, 282: 682-689 (1998). In this regard, techniques have been developed for the analysis of large populations of polynucleotides based either on specific hybridization of probes to microarrays, e.g. Lockhart et al. Hacia et al, Nature Genetics, 21: 4247 (1999), or on the counting of tags or signatures of DNA fragments, e.g. Velculescu et al, Science, 270: 484487 (1995); Brenner et al, Nature Biotechnology, 18: 630-634 (2000). These techniques have been used in discovery research to identify subsets of genes that have coordinated patterns of expression under a variety of circumstances or that are correlated with, and predictive of events, of interest, such as toxicity, drug responsiveness, risk of relapse, and the like, e.g. Golub et al, Science, 286: 531-537 (1999); Alizadeh et al, Nature, 403: 503-511 (2000); Perou et al, Nature, 406: 747-752 (2000); Shipp et al, Nature Medicine, 8: 68-74 (2002); Hakak et al, Proc. Natl. Acad. Sci., 98: 47454751 (2001); Thomas et al, Mol. Pharmacol., 60: 1189-1194 (2001); De Primo et al, BMC Cancer 2003, 3:3; and the like. Not infrequently the subset of genes found to be relevant has a size in the range of from ten or under to a few hundred.

In addition to gene expression, techniques have also been developed to measure genome-wide variation in gene copy number. For example, in the field of oncology, there is interest in measuring genome-wide copy number variation of local regions that characterize many cancers and that may have diagnostic or prognostic implications. For a review see Zhang et al. Annu. Rev. Genomics Hum. Genet. 2009. 10:451-81.

While such hybridization-based techniques offer the advantages of scale and the capability of detecting a wide range of gene expression or copy number levels, such measurements may be subject to variability relating to probe hybridization differences and cross-reactivity, element-to-element differences within microarrays, and microarray-to-microarray differences, Audic and Claverie, Genomic Res., 7: 986-995 (1997); Wittes and Friedman, J. Natl. Cancer Inst. 91: 400-401 (1999).

On the other hand, techniques that provide digital representations of abundance, such as SAGE (Velculescu et al, cited above) or MPSS (Brenner et al, cited above), are statistically more robust; they do not require repetition or standardization of counting experiments as counting statistics are well-modeled by the Poisson distribution, and the precision and accuracy of relative abundance measurements may be increased by increasing the size of the sample of tags or signatures counted, e.g. Audic and Claverie (cited above).

Both digital and non-digital hybridization-based assays have been implemented using oligonucleotide tags that are hybridized to their complements, typically as part of a detection or signal generation schemes that may include solid phase supports, such as microarrays, microbeads, or the like, e.g. Brenner et al, Proc. Natl. Acad. Sci., 97: 1665-1670 (2000); Church et al, Science, 240: 185-188 (1988); Chee, Nucleic Acids Research, 19: 3301-3305 (1991); Shoemaker et al., Nature Genetics, 14: 450456 (1996); Wallace, U.S. Pat. No. 5,981,179; Gerry et al, J. Mol. Biol., 292: 251-262 (1999); Fan et al., Genome Research, 10: 853-860 (2000); Ye et al., Human Mutation, 17: 305-316 (2001); and the like. Bacterial transcript imaging by hybridization of total RNA to nucleic acid arrays may be conducted as described in Saizieu et al., Nature Biotechnology, 16:45-48 (1998). Accessing genetic information using high density DNA arrays is further described in Chee et al., Science 274:610-614 (1996). Tagging approaches have also been used in combination with next-generation sequencing methods, see for example, Smith et al. NAR (May 11, 2010), 1-7.

A common feature among all of these approaches is a one-to-one correspondence between probe sequences and oligonucleotide tag sequences. That is, the oligonucleotide tags have been employed as probe surrogates for their favorable hybridizations properties, particularly under multiplex assay conditions.

Determining small numbers of biological molecules and their changes is essential when unraveling mechanisms of cellular response, differentiation or signal transduction, and in performing a wide variety of clinical measurements. Although many analytical methods have been developed to measure the relative abundance of different molecules through sampling (e.g., microarrays and sequencing), few techniques are available to determine the absolute number of molecules in a sample. This can be an important goal, for example in single cell measurements of copy number or stochastic gene expression, and is especially challenging when the number of molecules of interest is low in a background of many other species. As an example, measuring the relative copy number or expression level of a gene across a wide number of genes can currently be performed using PCR, hybridization to a microarray or by direct sequence counting. PCR and microarray analysis rely on the specificity of hybridization to identify the target of interest for amplification or capture respectively, then yield an analog signal proportional to the original number of molecules. A major advantage of these approaches is in the use of hybridization to isolate the specific molecules of interest within the background of many other molecules, generating specificity for the readout or detection step. The disadvantage is that the readout signal to noise is proportional to all molecules (specific and non-specific) specified by selective amplification or hybridization. The situation is reversed for sequence counting. No intended sequence specificity is imposed in the sequence capture step, and all molecules are sequenced. The major advantage is that the detection step simply yields a digital list of those sequences found, and since there is no specificity in the isolation step, all sequences must be analyzed at a sufficient statistical depth in order to learn about a specific sequence. Although very major technical advances in sequencing speed and throughput have occurred, the statistical requirements imposed to accurately measure small changes in concentration of a specific gene within the background of many other sequences requires measuring many sequences that don’t matter to find the ones that do matter. Each of these techniques, PCR, array hybridization and sequence counting is a comparative technique in that they primarily measure relative abundance, and do not typically yield an absolute number of molecules in a solution. A method of absolute counting of nucleic acids is digital PCR (B. Vogelstein, K. W. Kinzler, Proc Natl Acad Sci USA 96, 9236 (Aug. 3, 1999)), where solutions are progressively diluted into individual compartments until there is an average probability of one molecule per two wells, then detected by PCR. Although digital PCR can be used as a measure of absolute abundance, the dilutions must be customized for each type of molecule, and thus in practice is generally limited to the analysis of a small number of different molecules.

SUMMARY OF THE INVENTION

High-sensitivity single molecule digital counting by the stochastic labeling of a collection of identical molecules is disclosed. Each copy of a molecule randomly chooses from a non-depleting reservoir of diverse labels. The uniqueness of each labeled molecule is determined by the statistics of random choice, and depends on the number of copies of identical molecules in the collection compared to the diversity of labels. The size of the resulting set of labeled molecules is determined by the stochastic nature of the labeling process, and analysis reveals the original number of molecules. When the number of copies of a molecule to the diversity of labels is low, the labeled molecules are highly unique, and the digital counting efficiency is high. This stochastic transformation relaxes the problem of counting molecules from one of locating and identifying identical molecules to a series of yes/no digital questions detecting whether preprogrammed labels are present. The conceptual framework for stochastic mapping of a variety of molecule types is developed and the utility of the methods are demonstrated by stochastically labeling 360,000 different fragments of the human genome. The labeled fragments for a target molecule of choice are detected with high specificity using a microarray readout system, and with DNA sequencing. The results are consistent with a stochastic process, and yield highly precise relative and absolute counting statistics of selected molecules within a vast background of other molecules.

Methods are disclosed herein for digital counting of individual molecules of one or more targets. In preferred embodiments the targets are nucleic acids, but may be a variety of biological or non-biological elements. Targets are labeled so that individual occurrences of the same target are marked by attachment of a different label to difference occurrences. The attachment of the label confers a separate, determinable identity to each occurrence of targets that may otherwise be indistinguishable. Preferably the labels are different sequences that tag or mark each target occurrence uniquely. The resulting modified target comprises the target sequence and the unique identifier (which may be referred to herein as tag, counter, label, or marker). The junction of the target and identifier forms a uniquely detectable mechanism for counting the occurrence of that copy of the target. The attachment of the identifier to each occurrence of the target is a random sampling event. Each occurrence of target could choose any of the labels. Each identifier is present in multiple copies so selection of one copy does not remove that identifier sequence from the pool of identifiers so it is possible that the same identifier will be selected twice. The probability of that depends on the number of target occurrences relative to the number of different identifier sequences.

Each stochastic attachment event, where a target occurrence is attached to a unique identifier, results in the creation of a novel sequence formed at the junction of the identifier and the target. For a given target, all resulting products will contain the same target portion, but each will contain a different identifier sequence (T1L1, T1L2, ...T1LN where N is the number of different occurrences of target 1, “T1” and L is the identifier, L1, L2...LN). In preferred aspects the occurrences are detected by hybridization. In some aspects the methods and systems include a probe array comprising features, wherein each feature has a different combination of target sequence with identifiers, 1 to N wherein N is the number of unique identifiers in the pool of identifiers. The array has N features for each target, so if there are 8 targets to be analyzed there are 8 times N features on the array to interrogate the 8 targets.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic of a method of stochastic labeling and counting by hybridization to an array of support bound probes.

FIG. 2A shows a schematic of labeling target molecules with a pool of labels.

FIG. 2B shows a schematic of detection of labeled targets on an array having features that are label specific and target specific.

FIG. 3 shows a schematic of a method for circularizing targets and amplifying with gene specific primers.

FIG. 4 shows a schematic of a method for detection of ligation products by hybridization to array probes that are complementary to the sequence resulting from the ligation.

FIG. 5 shows a schematic of a method for target preparation.

FIG. 6 shows a method for stochastic counting by fragmentation where the unique end of the fragment is the label used for counting.

FIG. 7 provides an example of a genomic target ligated at either end to a label adaptor.

FIG. 8 shows a schematic of the arrangement and position of the adaptors, PCR primers, and the biotinylated array-ligation probe in one exemplary sample prep method.

FIG. 9 is a schematic of a method for using ligation based read out on arrays to detect labeled targets and minimize partial target hybridization.

FIG. 10 shows the arrangement of the adaptors, labels and primers used to convert the labeled sample into sequencing template.

FIG. 11 is a plot of the number of labels from a non-depleting reservoir of 960 lables that are predicted to be captures at least once, exactly once or exactly twice.

FIG. 12 is a plot of counting results for 4 different DNA copy number titrations using microarray hybridization (on left) or DNA sequencing in (on right).

FIG. 13 shows relative copy ratios of three tested gene targets representing copy number 1, 2 or 3 at different dilutions as analyzed using the disclosed methods.

FIG. 14 shows a comparison between experimentally observed label usage with those predicted from stochastic modeling.

FIG. 15 shows a plot of the expected label usage (y-axis) when ligating to a given number of target molecules (x-axis).

FIG. 16 shows a plot of number of target molecules (x-axis) compared to counting efficiency (y-axis).

FIG. 17 shows a schematic of a method for attaching labels to targets using a splint having a variable region.

FIG. 18 shows a schematic of a method for enriching for molecules that contain labels, target or both.

FIG. 19 shows a scatter plot of a series of different target plus label combinations.

FIG. 20 shows a plot of counting efficiency versus copies of target as the number of labels varies. The inset is a magnification of the upper left portion of the graph.

FIG. 21 is a plot of labels the array intensity observed compared to the number of fragments when fragments are binned according to size.

FIG. 22 shows labels observed by microarray hybridization plotted against intensity (y-axis) for each of 960 labels for the Chr 4 gene target.

FIG. 23 shows frequency plots (y-axis, log-scale) of intensity distributions of the 960 labels in the microarray experiments with the counting threshold applied indicated by the dashed line.

FIG. 24 shows plots showing fragment size distribution and mean raw intensity on chr22 tiling probes on the “CNVtype” array.

FIG. 25 shows a simulated PCR run showing the replication outcome for 500 molecules of a target fragment ligated to a library of 960 label counters.

FIG. 26 shows intensities of 1,152 array probes associated with a single gene target on chromosome 4 in the upper panel and a histogram of the intensity data corresponding to 960 labels in the lower panel.

FIG. 27 shows a plot of the number of times each of the 960 labels was observed in ligations with low DNA target amounts.

FIG. 28 shows an example of a replication process on a collection of 390 uniquely labeled target molecules resulting from 960 diverse labels independently marked with 500 copies of a target molecule.

FIG. 29 shows plots of labels observed in the mapped reads from the first sequencing run for chromosome 4 with the horizontal dashed line indicating the counting threshold applied and the vertical dashed line indicating the break separating the 192 negative controls from the expected labels (controls to the right of the line).

DETAILED DESCRIPTION OF THE INVENTION

Reference will now be made in detail to exemplary embodiments of the invention. While the invention will be described in conjunction with the exemplary embodiments, it will be understood that they are not intended to limit the invention to these embodiments. On the contrary, the invention is intended to cover alternatives, modifications and equivalents, which may be included within the spirit and scope of the invention.

The invention has many preferred embodiments and relies on many patents, applications and other references for details known to those of the art. Therefore, when a patent, application, or other reference, such as a printed publication, is cited or repeated below, it should be understood that it is incorporated by reference in its entirety for all purposes and particularly for the proposition that is recited.

As used in this application, the singular form “a,” “an,” and “the” include plural references unless the context clearly dictates otherwise. For example, the term “an agent” includes a plurality of agents, including mixtures thereof

An individual is not limited to a human being, but may also be other organisms including, but not limited to, mammals, plants, bacteria, or cells derived from any of the above.

Throughout this disclosure, various aspects of this invention can be presented in a range format. It should be understood that the description in range format is merely for convenience and brevity and should not be construed as an inflexible limitation on the scope of the invention. Accordingly, the description of a range should be considered to have specifically disclosed all the possible subranges as well as individual numerical values within that range. For example, description of a range such as from 1 to 6 should be considered to have specifically disclosed subranges such as from 1 to 3, from 1 to 4, from 1 to 5, from 2 to 4, from 2 to 6, from 3 to 6 etc., as well as individual numbers within that range, for example, 1, 2, 3, 4, 5, and 6. This applies regardless of the breadth of the range.

The practice of the present invention may employ, unless otherwise indicated, conventional techniques and descriptions of organic chemistry, polymer technology, molecular biology (including recombinant techniques), cell biology, biochemistry, and immunology, which are within the skill of the art. Such conventional techniques include polymer array synthesis, hybridization, ligation, and detection of hybridization using a label. Specific illustrations of suitable techniques can be had by reference to the example herein below. However, other equivalent conventional procedures can, of course, also be used. Such conventional techniques and descriptions can be found in standard laboratory manuals such as Genome Analysis: A Laboratory Manual Series (Vols. I-IV), Using Antibodies: A Laboratory Manual, Cells: A Laboratory Manual, PCR Primer: A Laboratory Manual, and Molecular Cloning: A Laboratory Manual (all from Cold Spring Harbor Laboratory Press), Gait, “Oligonucleotide Synthesis: A Practical Approach” 1984, IRL Press, London, Nelson and Cox (2000), Lehninger et al., (2008) Principles of Biochemistry 5th Ed., W.H. Freeman Pub., New York, NY and Berg et al. (2006) Biochemistry, 6^(th) Ed., W.H. Freeman Pub., New York, NY, all of which are herein incorporated in their entirety by reference for all purposes.

The present invention can employ solid substrates, including arrays in some preferred embodiments. Methods and techniques applicable to polymer (including protein) array synthesis have been described in U.S. Pat. Pub. No. 20050074787, WO 00/58516, U.S. Pat. Nos. 5,143,854, 5,242,974, 5,252,743, 5,324,633, 5,384,261, 5,405,783, 5,424,186, 5,451,683, 5,482,867, 5,491,074, 5,527,681, 5,550,215, 5,571,639, 5,578,832, 5,593,839, 5,599,695, 5,624,711, 5,631,734, 5,795,716, 5,831,070, 5,837,832, 5,856,101, 5,858,659, 5,936,324, 5,968,740, 5,974,164, 5,981,185, 5,981,956, 6,025,601, 6,033,860, 6,040,193, 6,090,555, 6,136,269, 6,269,846 and 6,428,752, in PCT Publication No. WO 99/36760 and WO 01/58593, which are all incorporated herein by reference in their entirety for all purposes.

Patents that describe synthesis techniques in specific embodiments include U.S. Pat. Nos. 5,412,087, 6,147,205, 6,262,216, 6,310,189, 5,889,165, and 5,959,098. Nucleic acid arrays are described in many of the above patents, but the same techniques may be applied to polypeptide arrays.

The present invention also contemplates many uses for polymers attached to solid substrates. These uses include gene expression monitoring, profiling, library screening, genotyping and diagnostics. Gene expression monitoring and profiling methods can be shown in U.S. Pat. Nos. 5,800,992, 6,013,449, 6,020,135, 6,033,860, 6,040,138, 6,177,248 and 6,309,822. Genotyping and uses therefore are shown in U.S. Pat. Publication Nos. 20030036069 and 20070065816 and U.S. Pat. Nos. 5,856,092, 6,300,063, 5,858,659, 6,284,460, 6,361,947, 6,368,799 and 6,333,179. Other uses are embodied in U.S. Pat. Nos. 5,871,928, 5,902,723, 6,045,996, 5,541,061, and 6,197,506.

The present invention also contemplates sample preparation methods in certain embodiments. Prior to or concurrent with analysis, the sample may be amplified by a variety of mechanisms. In some aspects nucleic acid amplification methods such as PCR may be combined with the disclosed methods and systems. See, for example, PCR Technology: Principles and Applications for DNA Amplification (Ed. H.A. Erlich, Freeman Press, NY, NY, 1992); PCR Protocols: A Guide to Methods and Applications (Eds. Innis, et al., Academic Press, San Diego, CA, 1990); Mattila et al., Nucleic Acids Res. 19, 4967 (1991); Eckert et al., PCR Methods and Applications 1, 17 (1991); PCR (Eds. McPherson et al., IRL Press, Oxford); and U.S. Pat. Nos. 4,683,202, 4,683,195, 4,800,159, 4,965,188, and 5,333,675, each of which is incorporated herein by reference in their entireties for all purposes. Enzymes and related methods of use in molecular biology that may be used in combination with the disclosed methods and systems are reviewed, for example, in Rittie and Perbal, J. Cell Commun. Signal. (2008) 2:25-45. The sample may be amplified on the array. See, for example, U.S. Pat. No. 6,300,070 and which is incorporated herein by reference in its entirety for all purposes.

Many of the methods and systems disclosed herein utilize enzyme activities. A variety of enzymes are well known, have been characterized and many are commercially available from one or more supplier. For a review of enzyme activities commonly used in molecular biology see, for example, Rittie and Perbal, J. Cell Commun. Signal. (2008) 2:25-45, incorporated herein by reference in its entirety. Exemplary enzymes include DNA dependent DNA polymerases (such as those shown in Table 1 of Rittie and Perbal), RNA dependent DNA polymerase (see Table 2 of Rittie and Perbal), RNA polymerases, ligases (see Table 3 of Rittie and Perbal), enzymes for phosphate transfer and removal (see Table 4 of Rittie and Perbal), nucleases (see Table 5 of Rittie and Perbal), and methylases.

Other methods of genome analysis and complexity reduction include, for example, AFLP, see U.S. Pat. 6,045,994, which is incorporated herein by reference, and arbitrarily primed-PCR (AP-PCR) see McClelland and Welsh, in PCR Primer: A laboratory Manual, (1995) eds. C. Dieffenbach and G. Dveksler, Cold Spring Harbor Lab Press, for example, at p 203, which is incorporated herein by reference in its entirety. Additional methods of sample preparation and techniques for reducing the complexity of a nucleic sample are described in Dong et al., Genome Research 11, 1418 (2001), in U.S. Pat. No. 6,361,947, 6,391,592, 6,458,530 and U.S. Pat. Publication Nos. 20030039069, 20050079536, 20030096235, 20030082543, 20040072217, 20050142577, 20050233354, 20050227244, 20050208555, 20050074799, 20050042654 and 20040067493, which are each incorporated herein by reference in their entireties.

The design and use of allele-specific probes for analyzing polymorphisms is described by e.g., Saiki et al., Nature 324, 163-166 (1986); Dattagupta, EP 235,726, and WO 89/11548. Allele-specific probes can be designed that hybridize to a segment of target DNA from one individual but do not hybridize to the corresponding segment from another individual due to the presence of different polymorphic forms in the respective segments from the two individuals.

Sample preparation methods are also contemplated in many embodiments. Prior to or concurrent with analysis, the genomic sample may be amplified by a variety of mechanisms, some of which may employ PCR. See, e.g., PCR Technology: Principles and Applications for DNA Amplification (Ed. H.A. Erlich, Freeman Press, NY, NY, 1992); PCR Protocols: A Guide to Methods and Applications (Eds. Innis, et al., Academic Press, San Diego, CA, 1990); Mattila et al., Nucleic Acids Res. 19, 4967 (1991); Eckert et al., PCR Methods and Applications 1, 17 (1991); PCR (Eds. McPherson et al., IRL Press, Oxford); and U.S. Pat. Nos. 4,683,202, 4,683,195, 4,800,159 4,965,188, and 5,333,675, and each of which is incorporated herein by reference in their entireties for all purposes. See also U.S. Pat. No. 6,300,070 which is incorporated herein by reference. Additional methods of sample preparation and techniques for reducing the complexity of a nucleic sample are described in Dong et al., Genome Research 11, 1418 (2001), in U.S. Pat. No. 6,361,947, 6,391,592 and U.S. Pat. Pub. Nos. 20030096235, 20030082543 and 20030036069.

Other suitable amplification methods include the ligase chain reaction (LCR) (for example, Wu and Wallace, Genomics 4, 560 (1989), Landegren et al., Science 241, 1077 (1988) and Barringer et al. Gene 89:117 (1990)), transcription amplification (Kwoh et al., Proc. Natl. Acad. Sci. USA 86, 1173 (1989) and WO88/10315), self-sustained sequence replication (Guatelli et al., Proc. Nat. Acad. Sci. USA, 87, 1874 (1990) and WO90/06995), selective amplification of target polynucleotide sequences (U.S. Pat. No. 6,410,276), consensus sequence primed polymerase chain reaction (CP-PCR) (U.S. Pat. No. 4,437,975), arbitrarily primed polymerase chain reaction (AP-PCR) (U.S. Pat. Nos. 5,413,909, 5,861,245), rolling circle amplification (RCA) (for example, Fire and Xu, PNAS 92:4641 (1995) and Liu et al., J. Am. Chem. Soc. 118:1587 (1996)) and nucleic acid based sequence amplification (NABSA). (See, U.S. Pat. Nos. 5,409,818, 5,554,517, and 6,063,603, each of which is incorporated herein by reference). Other amplification methods that may be used are described in, U.S. Pat. Nos. 6,582,938, 5,242,794, 5,494,810, 4,988,617, and US Pub. No. 20030143599 each of which is incorporated herein by reference.

Molecular inversion probes may also be used for amplification of selected targets. MIPs may be generated so that the ends of the pre-circle probe are complementary to regions that flank the region to be amplified. The gap can be closed by extension of the end of the probe so that the complement of the target is incorporated into the MIP prior to ligation of the ends to form a closed circle. The closed circle can be amplified as previously disclosed in Hardenbol et al., Genome Res. 15:269-275 (2005) and in U.S. Pat. No. 6,858,412.

In some embodiments, amplification may include the use of a strand displacing polymerase that may be primed by selected primers or by a mixture of primers, for example, random hexamers. See for example Lasken and Egholm, Trends Biotechnol. 2003 21(12):531-5; Barker et al. Genome Res. 2004 May;14(5):901-7; Dean et al. Proc Natl Acad Sci U S A. 2002; 99(8):5261-6; and Paez, J.G., et al. Nucleic Acids Res. 2004; 32(9):e71. Other amplification methods that may be used include: Qbeta Replicase, described in PCT Patent Application No. PCT/US87/00880, isothermal amplification methods such as SDA, described in Walker et al. 1992, Nucleic Acids Res. 20(7):1691-6, 1992, and rolling circle amplification, described in U.S. Pat. No. 5,648,245. DNA may also be amplified by multiplex locus-specific PCR or using adaptor-ligation and single primer PCR. Other available methods of amplification, such as balanced PCR (Makrigiorgos, et al. (2002), Nat Biotechnol, Vol. 20, pp.936-9), may also be used.

Methods of ligation will be known to those of skill in the art and are described, for example in Sambrook et at. (2001) and the New England BioLabs catalog both of which are incorporated herein by reference for all purposes. Methods include using T4 DNA Ligase which catalyzes the formation of a phosphodiester bond between juxtaposed 5′ phosphate and 3′ hydroxyl termini in duplex DNA or RNA with blunt and sticky ends; Taq DNA Ligase which catalyzes the formation of a phosphodiester bond between juxtaposed 5′ phosphate and 3′ hydroxyl termini of two adjacent oligonucleotides which are hybridized to a complementary target DNA; E. coli DNA ligase which catalyzes the formation of a phosphodiester bond between juxtaposed 5′-phosphate and 3′-hydroxyl termini in duplex DNA containing cohesive ends; and T4 RNA ligase which catalyzes ligation of a 5′ phosphoryl-terminated nucleic acid donor to a 3′ hydroxyl-terminated nucleic acid acceptor through the formation of a 3′->5′ phosphodiester bond, substrates include single-stranded RNA and DNA as well as dinucleoside pyrophosphates; or any other methods described in the art. Fragmented DNA may be treated with one or more enzymes, for example, an endonuclease, prior to ligation of adaptors to one or both ends to facilitate ligation by generating ends that are compatible with ligation.

Fixed content mapping arrays are available from Affymetrix, for example, the SNP 6.0 array. Methods for using mapping arrays see, for example, Kennedy et al., Nat. Biotech. 21:1233-1237 (2003), Matsuzaki et al., Genome Res. 14:414-425 (2004), Matsuzaki et al., Nat. Meth. 1:109-111 (2004) and U.S. Pat. Pub. Nos. 20040146890 and 20050042654, each incorporated herein by reference. Applications of microarrays for SNP genotyping have been described in e.g., U.S. Pat. Nos 6,300,063, 6,361,947, 6,368,799 and US Pat. Publication Nos. 20040067493, 20030232353, 20030186279, 20050260628, 20070065816 and 20030186280, all incorporated herein by reference in their entireties for all purposes.

Selected panels of SNPs can also be interrogated using a panel of locus specific probes in combination with a universal array as described in Hardenbol et al., Genome Res. 15:269-275 (2005) and in U.S. Pat. No. 6,858,412. Universal tag arrays and reagent kits for performing such locus specific genotyping using panels of custom molecular inversion probes (MIPs) are available from Affymetrix.

Computer implemented methods for determining genotype using data from mapping arrays are disclosed, for example, in Liu, et al., Bioinformatics 19:2397-2403 (2003), Rabbee and Speed, Bioinformatics, 22:7-12 (2006), and Di et al., Bioinformatics 21:1958-63 (2005). Computer implemented methods for linkage analysis using mapping array data are disclosed, for example, in Ruschendorf and Nurnberg, Bioinformatics 21:2123-5 (2005) and Leykin et al., BMC Genet. 6:7, (2005). Computer methods for analysis of genotyping data are also disclosed in U.S. Pat. Pub. Nos. 20060229823, 20050009069, 20040138821, 20060024715, 20050250151 and 20030009292.

Methods for analyzing chromosomal copy number using mapping arrays are disclosed, for example, in Bignell et al., Genome Res. 14:287-95 (2004), Lieberfarb, et al., Cancer Res. 63:4781-4785 (2003), Zhao et al., Cancer Res. 64:3060-71 (2004), Huang et al., Hum Genomics 1:287-299 (2004), Nannya et al., Cancer Res. 65:6071-6079 (2005), Slater et al., Am. J. Hum. Genet. 77:709-726 (2005) and Ishikawa et al., Biochem. and Biophys. Res. Comm., 333:1309-1314 (2005). Computer implemented methods for estimation of copy number based on hybridization intensity are disclosed in U.S. Pat. Pub. Nos. 20040157243, 20050064476, 20050130217, 20060035258, 20060134674 and 20060194243.

Additional methods of sample preparation and techniques for reducing the complexity of a nucleic sample are described in Dong et al., Genome Research 11, 1418 (2001), in U.S. Pat. Nos. 6,361,947, 6,391,592 and 6,872,529 and U.S. Pat. Publication Nos. 20030036069, 20030096235 and 20030082543. Additional methods of using a genotyping array are disclosed, for example, in U.S. Pat. Publication Nos. 20040146883, 20030186280, 20030186279, 20040067493, 20030232353, 20060292597, 20050233354, 20050074799, 20070065816 and 20040185475.

Methods for conducting polynucleotide hybridization assays have been well developed in the art. Hybridization assay procedures and conditions will vary depending on the application and are selected in accordance with known general binding methods, including those referred to in: Maniatis et al. Molecular Cloning: A Laboratory Manual (2^(nd) Ed. Cold Spring Harbor, N.Y, 1989); Berger and Kimmel Methods in Enzymology, Vol. 152, Guide to Molecular Cloning Techniques (Academic Press, Inc., San Diego, CA, 1987); Young and Davis, P.N.A.S, 80: 1194 (1983). Methods and apparatus for carrying out repeated and controlled hybridization reactions have been described in U.S. Pat. Nos. 5,871,928, 5,874,219, 6,045,996 and 6,386,749, 6,391,623 each of which are incorporated herein by reference.

The present invention also contemplates signal detection of hybridization between ligands in certain preferred embodiments. See U.S. Pat. Nos. 5,143,854, 5,578,832, 5,631,734, 5,834,758, 5,936,324, 5,981,956, 6,025,601, 6,141,096, 6,185,030, 6,201,639, 6,218,803, and 6,225,625 in U.S. Pat. Pub. No. 20040012676 and in PCT Application PCT/US99/06097 (published as WO99/47964), each of which also is hereby incorporated by reference in its entirety for all purposes.

Methods and apparatus for signal detection and processing of intensity data are disclosed in, for example, U.S. Pat. Nos. 5,143,854, 5,547,839, 5,578,832, 5,631,734, 5,800,992, 5,834,758, 5,856,092, 5,902,723, 5,936,324, 5,981,956, 6,025,601, 6,090,555, 6,141,096, 6,185,030, 6,201,639; 6,218,803; and 6,225,625, in U.S. Pat. Pub. Nos. 20040012676 and 20050059062 and in PCT Application PCT/US99/06097 (published as WO99/47964), each of which also is hereby incorporated by reference in its entirety for all purposes.

The practice of the present invention may also employ conventional biology methods, software and systems. Computer software products of the invention typically include computer readable medium having computer-executable instructions for performing the logic steps of the method of the invention. Suitable computer readable medium include floppy disk, CD-ROM/DVD/DVD-ROM, hard-disk drive, flash memory, ROM/RAM, magnetic tapes, etc. The computer-executable instructions may be written in a suitable computer language or combination of several languages. Basic computational biology methods are described in, for example, Setubal and Meidanis et al., Introduction to Computational Biology Methods (PWS Publishing Company, Boston, 1997); Salzberg, Searles, Kasif, (Ed.), Computational Methods in Molecular Biology, (Elsevier, Amsterdam, 1998); Rashidi and Buehler, Bioinformatics Basics: Application in Biological Science and Medicine (CRC Press, London, 2000) and Ouelette and Bzevanis Bioinformatics: A Practical Guide for Analysis of Gene and Proteins (Wiley & Sons, Inc., 2^(nd) ed., 2001). See U.S. Pat. No. 6,420,108.

The present invention may also make use of various computer program products and software for a variety of purposes, such as probe design, management of data, analysis, and instrument operation. See, U.S. Pat. Nos. 5,593,839, 5,795,716, 5,733,729, 5,974,164, 6,066,454, 6,090,555, 6,185,561, 6,188,783, 6,223,127, 6,229,911 and 6,308,170. Computer methods related to genotyping using high density microarray analysis may also be used in the present methods, see, for example, US Pat. Pub. Nos. 20050250151, 20050244883, 20050108197, 20050079536 and 20050042654.

Additionally, the present disclosure may have preferred embodiments that include methods for providing genetic information over networks such as the Internet as shown in U.S. Pat. Pub. Nos. 20030097222, 20020183936, 20030100995, 20030120432, 20040002818, 20040126840, and 20040049354.

An allele refers to one specific form of a genetic sequence (such as a gene) within a cell, an individual or within a population, the specific form differing from other forms of the same gene in the sequence of at least one, and frequently more than one, variant sites within the sequence of the gene. The sequences at these variant sites that differ between different alleles are termed “variances”, “polymorphisms”, or “mutations”. At each autosomal specific chromosomal location or “locus” an individual possesses two alleles, one inherited from one parent and one from the other parent, for example one from the mother and one from the father. An individual is “heterozygous” at a locus if it has two different alleles at that locus. An individual is “homozygous” at a locus if it has two identical alleles at that locus.

Single nucleotide polymorphisms (SNPs) are positions at which two alternative bases occur at appreciable frequency (>1%) in a given population. SNPs are a common type of human genetic variation and are useful in the performance of genome wide association studies (GWAS). GWAS may be used, for example for the analysis of biological pathways, see Wang and Hakonarson, Nat. Rev. Genet. 2010, 11:843-854. Other common variation includes single base deletions or insertions of a nucleotide relative to a reference allele. Copy number variants (CNVs), transversions and other rearrangements are also forms of genetic variation.

The term genotyping refers to the determination of the genetic information an individual carries at one or more positions in the genome. For example, genotyping may comprise the determination of which allele or alleles an individual carries for a single SNP or the determination of which allele or alleles an individual carries for a plurality of SNPs or CNVs. A diploid individual may be homozygous for each of the two possible alleles (for example, AA or BB) or heterozygous (for example, AB). For additional information regarding genotyping and genome structure see, Color Atlas of Genetics, Ed. Passarge, Thieme, New York, NY (2001), which is incorporated by reference.

Normal cells that are heterozygous at one or more loci may give rise to tumor cells that are homozygous at those loci. This loss of heterozygosity (LOH) may result from structural deletion of normal genes or loss of the chromosome carrying the normal gene, mitotic recombination between normal and mutant genes, followed by formation of daughter cells homozygous for deleted or inactivated (mutant) genes; or loss of the chromosome with the normal gene and duplication of the chromosome with the deleted or inactivated (mutant) gene.

The term “array” as used herein refers to an intentionally created collection of molecules which can be prepared either synthetically or biosynthetically. The molecules in the array can be identical or different from each other. The array can assume a variety of formats, for example, libraries of soluble molecules; libraries of compounds tethered to resin beads, silica chips, microparticles, nanoparticles or other solid supports.

The term “complementary” as used herein refers to the hybridization or base pairing between nucleotides or nucleic acids, such as, for instance, between the two strands of a double stranded DNA molecule or between an oligonucleotide primer and a primer binding site on a single stranded nucleic acid to be sequenced or amplified. See, M. Kanehisa Nucleic Acids Res. 12:203 (1984), incorporated herein by reference.

The term “copy number variation” or “CNV” refers to differences in the copy number of genetic information. In many aspects it refers to differences in the per genome copy number of a genomic region. For example, in a diploid organism the expected copy number for autosomal genomic regions is 2 copies per genome. Such genomic regions should be present at 2 copies per cell. For a recent review see Zhang et al. Annu. Rev. Genomics Hum. Genet. 2009. 10:451-81. CNV is a source of genetic diversity in humans and can be associated with complex disorders and disease, for example, by altering gene dosage, gene disruption, or gene fusion. They can also represent benign polymorphic variants. CNVs can be large, for example, larger than 1 Mb, but many are smaller, for example between 100 bp and 1 Mb. More than 38,000 CNVs greater than 100 bp (and less than 3 Mb) have been reported in humans. Along with SNPs these CNVs account for a significant amount of phenotypic variation between individuals. In adition to having deleterious impacts, e.g. causing disease, they may also result in advantageous variation.

Digital PCR is a technique where a limiting dilution of the sample is made across a large number of separate PCR reactions so that most of the reactions have no template molecules and give a negative amplification result. Those reactions that are positive at the reaction endpoint are counted as individual template molecules present in the original sample in a 1 to 1 relationship. See Kalina et al. NAR 25:1999-2004 (1997) and Vogelstein and Kinzler, PNAS 96:9236-9241 (1999). This method is an absolute counting method where solutions are partitioned into containers until there is an average probability of one molecule per two containers or when, P₀ = (1-e^(-n/c)) = ½; where n is the number of molecules and c is the number of containers, or n/c is 0.693. Quantitative partitioning is assumed, and the dynamic range is governed by the number of containers available for stochastic separation. The molecules are then detected by PCR and the number of positive containers is counted. Each successful amplification is counted as one molecule, independent of the actual amount of product. PCR-based techniques have the additional advantage of only counting molecules that can be amplified, e.g. that are relevant to the massively parallel PCR step in the sequencing workflow. Because digital PCR has single molecule sensitivity, only a few hundred library molecules are required for accurate quantification. Elimination of the quantification bottleneck reduces the sample input requirement from micrograms to nanograms or less, opening the way for minute and/or precious samples onto the next-generation sequencing platforms without the distorting effects of pre-amplification. Digital PCR has been used to quantify sequencing libraries to eliminate uncertainty associated with the construction and application of standard curves to PCR-based quantification and enable direct sequencing without titration runs. See White et al. BMC Genomics 10: 116 (2009).

To vary dynamic range, micro-fabrication can be used to substantially increase the number of containers. See, Fan et al. Am J Obstet Gynecol 200, 543 el (May, 2009).

Similarly, in stochastic labeling as disclosed herein, the same statistical conditions are met when P₀ = (1-e^(-n/m)) = ½; where m is the number of labels, and one half of the labels will be used at least once when n/m = 0.693. The dynamic range is governed by the number of labels used, and the number of labels can be easily increased to extend the dynamic range. The number of containers in digital PCR plays the same role as the number of labels in stochastic labeling and by substituting containers for labels identical statistical equations may be applied. Using the principles of physical separation, digital PCR stochastically expands identical molecules into physical space, whereas the principle governing stochastic labeling is identity based and expands identical molecules into identity space.

The term “hybridization” as used herein refers to the process in which two single-stranded polynucleotides bind noncovalently to form a stable double-stranded polynucleotide; triple-stranded hybridization is also theoretically possible. The resulting (usually) double-stranded polynucleotide is a “hybrid.” The proportion of the population of polynucleotides that forms stable hybrids is referred to herein as the “degree of hybridization.” Hybridizations may be performed under stringent conditions, for example, at a salt concentration of no more than 1 M and a temperature of at least 25° C. For example, conditions of 5X SSPE (750 mM NaC1, 50 mM NaPhosphate, 5 mM EDTA, pH 7.4) and a temperature of 25-30° C. are suitable for allele-specific probe hybridizations. For stringent conditions, see, for example, Sambrook, Fritsche and Maniatis. “Molecular Cloning A laboratory Manual” 2nd Ed. Cold Spring Harbor Press (1989) which is hereby incorporated by reference in its entirety for all purposes above. In some aspects salt concentrations for hybridization are preferably between about 200 mM and about 1 M or between about 200 mM and about 500 mM. Hybridization temperatures can be as low as 5° C., but are typically greater than 22° C., more typically greater than about 30° C., and preferably in excess of about 37° C. Longer fragments may require higher hybridization temperatures for specific hybridization. As other factors may affect the stringency of hybridization, including base composition and length of the complementary strands, presence of organic solvents and extent of base mismatching, the combination of parameters is more important than the absolute measure of any one alone.

The term “mRNA” or sometimes refer by “mRNA transcripts” as used herein, include, but not limited to pre-mRNA transcript(s), transcript processing intermediates, mature mRNA(s) ready for translation and transcripts of the gene or genes, or nucleic acids derived from the mRNA transcript(s). Transcript processing may include splicing, editing and degradation. As used herein, a nucleic acid derived from an mRNA transcript refers to a nucleic acid for whose synthesis the mRNA transcript or a subsequence thereof has ultimately served as a template. Thus, a cDNA reverse transcribed from an mRNA, an RNA transcribed from that cDNA, a DNA amplified from the cDNA, an RNA transcribed from the amplified DNA, etc., are all derived from the mRNA transcript and detection of such derived products is indicative of the presence and/or abundance of the original transcript in a sample. Thus, mRNA derived samples include, but are not limited to, mRNA transcripts of the gene or genes, cDNA reverse transcribed from the mRNA, cRNA transcribed from the cDNA, DNA amplified from the genes, RNA transcribed from amplified DNA, and the like.

The term “nucleic acid” as used herein refers to a polymeric form of nucleotides of any length, either ribonucleotides, deoxyribonucleotides or peptide nucleic acids (PNAs), that comprise purine and pyrimidine bases, or other natural, chemically or biochemically modified, non-natural, or derivatized nucleotide bases. The backbone of the polynucleotide can comprise sugars and phosphate groups, as may typically be found in RNA or DNA, or modified or substituted sugar or phosphate groups. A polynucleotide may comprise modified nucleotides, such as methylated nucleotides and nucleotide analogs. The sequence of nucleotides may be interrupted by non-nucleotide components. Thus the terms nucleoside, nucleotide, deoxynucleoside and deoxynucleotide generally include analogs such as those described herein. These analogs are those molecules having some structural features in common with a naturally occurring nucleoside or nucleotide such that when incorporated into a nucleic acid or oligonucleoside sequence, they allow hybridization with a naturally occurring nucleic acid sequence in solution. Typically, these analogs are derived from naturally occurring nucleosides and nucleotides by replacing and/or modifying the base, the ribose or the phosphodiester moiety. The changes can be tailor made to stabilize or destabilize hybrid formation or enhance the specificity of hybridization with a complementary nucleic acid sequence as desired.

The term “oligonucleotide” or sometimes refer by “polynucleotide” as used herein refers to a nucleic acid ranging from at least 2, preferable at least 8, and more preferably at least 20 nucleotides in length or a compound that specifically hybridizes to a polynucleotide. Polynucleotides of the present invention include sequences of deoxyribonucleic acid (DNA) or ribonucleic acid (RNA) which may be isolated from natural sources, recombinantly produced or artificially synthesized and mimetics thereof. A further example of a polynucleotide of the present invention may be peptide nucleic acid (PNA). The invention also encompasses situations in which there is a nontraditional base pairing such as Hoogsteen base pairing which has been identified in certain tRNA molecules and postulated to exist in a triple helix. “Polynucleotide” and “oligonucleotide” are used interchangeably in this application.

The term “polymorphism” as used herein refers to the occurrence of two or more genetically determined alternative sequences or alleles in a population. A polymorphic marker or site is the locus at which divergence occurs. Preferred markers have at least two alleles, each occurring at frequency of greater than 1%, and more preferably greater than 10% or 20% of a selected population. A polymorphism may comprise one or more base changes, an insertion, a repeat, or a deletion. A polymorphic locus may be as small as one base pair. Polymorphic markers include restriction fragment length polymorphisms, variable number of tandem repeats (VNTR’s), hypervariable regions, minisatellites, dinucleotide repeats, trinucleotide repeats, tetranucleotide repeats, simple sequence repeats, and insertion elements such as Alu. The first identified allelic form is arbitrarily designated as the reference form and other allelic forms are designated as alternative or variant alleles. The allelic form occurring most frequently in a selected population is sometimes referred to as the wildtype form. Diploid organisms may be homozygous or heterozygous for allelic forms. A diallelic polymorphism has two forms. A triallelic polymorphism has three forms. Single nucleotide polymorphisms (SNPs) are included in polymorphisms.

The term “primer” as used herein refers to a single-stranded oligonucleotide capable of acting as a point of initiation for template-directed DNA synthesis under suitable conditions for example, buffer and temperature, in the presence of four different nucleoside triphosphates and an agent for polymerization, such as, for example, DNA or RNA polymerase or reverse transcriptase. The length of the primer, in any given case, depends on, for example, the intended use of the primer, and generally ranges from 15 to 30 nucleotides. Short primer molecules generally require cooler temperatures to form sufficiently stable hybrid complexes with the template. A primer need not reflect the exact sequence of the template but must be sufficiently complementary to hybridize with such template. The primer site is the area of the template to which a primer hybridizes. The primer pair is a set of primers including a 5′ upstream primer that hybridizes with the 5′ end of the sequence to be amplified and a 3′ downstream primer that hybridizes with the complement of the 3′ end of the sequence to be amplified.

The term “probe” as used herein refers to a surface-immobilized molecule that can be recognized by a particular target. See U.S. Pat. No. 6,582,908 for an example of arrays having all possible combinations of probes with 10, 12, and more bases. Examples of probes that can be investigated by this invention include, but are not restricted to, agonists and antagonists for cell membrane receptors, toxins and venoms, viral epitopes, hormones (for example, opioid peptides, steroids, etc.), hormone receptors, peptides, enzymes, enzyme substrates, cofactors, drugs, lectins, sugars, oligonucleotides, nucleic acids, oligosaccharides, proteins, and monoclonal antibodies.

The term “solid support”, “support”, and “substrate” as used herein are used interchangeably and refer to a material or group of materials having a rigid or semi-rigid surface or surfaces. In many embodiments, at least one surface of the solid support will be substantially flat, although in some embodiments it may be desirable to physically separate synthesis regions for different compounds with, for example, wells, raised regions, pins, etched trenches, or the like. According to other embodiments, the solid support(s) will take the form of beads, resins, gels, microspheres, or other geometric configurations. See U.S. Pat. No. 5,744,305 and U.S. Pat. Pub. Nos. 20090149340 and 20080038559 for exemplary substrates.

A stochastic process is the counterpart to a deterministic process. Instead of dealing with only one possible “reality” of how the process might evolve under time, in a stochastic or random process there is some indeterminacy in its future evolution described by probability distributions. This means that even if the initial condition (or starting point) is known, there are many possibilities the process might go to, but some paths are more probable and others less.

In the simplest possible case, a stochastic process amounts to a sequence of random variables known as a time series (for example, see Markov chain). Another basic type of a stochastic process is a random field, whose domain is a region of space, in other words, a random function whose arguments are drawn from a range of continuously changing values. One approach to stochastic processes treats them as functions of one or several deterministic arguments (“inputs”, in most cases regarded as “time”) whose values (“outputs”) are random variables: non-deterministic (single) quantities which have certain probability distributions. Random variables corresponding to various times (or points, in the case of random fields) may be completely different. The main requirement is that these different random quantities all have the same “type”. Although the random values of a stochastic process at different times may be independent random variables, in most commonly considered situations they exhibit complicated statistical correlations.

Familiar examples of processes modeled as stochastic time series include stock market and exchange rate fluctuations, signals such as speech, audio and video, medical data such as a patient’s EKG, EEG, blood pressure or temperature, and random movement such as Brownian motion or random walks. Examples of random fields include static images, random terrain (landscapes), or composition variations of an heterogeneous material.

The stochastic labeling process can be generalized as follows. Consider n copies of a given target molecule T, where T = {t1, i = 1,2, ..., n}, and a non-depleting reservoir of m diverse labels L, where L = {l_(j), j = 1,2, ..., m}. T reacts with L stochastically, such that each t_(i) will choose exactly one l_(j(i)), 1 ≤j(i) ≤m to take on a new identity t_(i)l_(j(i)), and may be identified by its label subscript. Therefore, the new collection of molecules T* may be denoted as T* = {tl_(j(i)), i = 1,2, ..., n, 1 ≤j(i) ≤m}.

When different copies of the target molecules react with the same label, j(i) for those molecules will assume the same value, therefore, the number of uniquely labeled target molecules k cannot be greater than m. The stochastic mapping of the set of labels on a target may be described by a stochastic operator S with m members, acting upon a target population of n, such that S(m)T(n) = T *(m,n) generating the set T* = {tl_(j(i)), i = 1,2, ..., n, 1 ≤j(i) ≤m}. For simplicity, we may write T*= {t1_(k)}. Furthermore, since S operates on all molecules randomly, it will independently act on many different target sequences and the method can be expanded to count copies of multiple target sequences, w, simultaneously:

ST^(w) =ST₁ + ST₂ + ... + ST_(w) = T₁* + T₂* + ... + T_(w)* = {tl_(k)}₁ + {tl_(k)}₂ + ... + {tl_(k)}_(w), where each T_(i)*, i = 1,2, ..., w consists of a set {tl_(k)}_(i). The net result of S operating on a specific target population is to map the number of molecules, n, of that target, to the number of labels captured, k, which is a random variable.

Since target molecules randomly react with a label with probability

$\frac{1}{m},$

the probability of a label being captured by exactly x out of n copies of a target molecule can be modeled as a Binomial distribution,

$P(x) = \frac{n!}{x!\left( {n - x} \right)!}\left( \frac{1}{m} \right)^{x}\left( {1 - \frac{1}{m}} \right)^{n - x},$

where x! denotes the factorial of x. The probability that a label will not be captured by any copy of the target molecule is P(0) = (1-1/m)^(n), and the probability that a label will be captured at least once is 1-P(0). When n →∞ and 1/m → 0 in the way that n / m → λ, P(x) converges to the Poisson distribution with mean λ, i.e.,

$P(x) = \frac{\lambda^{x}}{x!}e^{- \lambda}.$

To compute the number of unique labels captured by n copies of a target molecule, we introduce an index random variable, X_(i), which is 1 if a label has been captured at least once, and 0 otherwise. The number of unique labels captured is thus

$k = {\sum\limits_{i = 1}^{m}X_{i}}.$

The mean and variance of k can be derived,

$\begin{matrix} {E\lbrack k\rbrack = m\left\lbrack {1 - \left( {1 - \frac{1}{m}} \right)^{n}} \right\rbrack} & \text{­­­(1)} \end{matrix}$

$\begin{matrix} \begin{array}{l} {\text{Var}\lbrack k\rbrack =} \\ {m\left\lbrack {1 - \left( {1 - \frac{1}{m}} \right)^{n}} \right\rbrack\left( {1 - \frac{1}{m}} \right)^{n} + m\left( {m - 1} \right)\left\lbrack {\left( {1 - \frac{2}{m}} \right)^{n} - \left( {1 - \frac{1}{m}} \right)^{2n}} \right\rbrack} \end{array} & \text{­­­(2)} \end{matrix}$

Similarly, to compute the number of labels captured by exactly x copies of a target molecule, we introduce another index random variable, Y_(i), which is 1 if a label has been captured exactly x times, and 0 otherwise. The number of labels captured x times is thus

$t = {\sum\limits_{i = 1}^{m}Y_{i}}.$

The mean and variance of t are,

$\begin{matrix} {E\lbrack t\rbrack = \frac{m \cdot n!}{x!\left( {n - x} \right)!}\left( \frac{1}{m} \right)^{x}\left( {1 - \frac{1}{m}} \right)^{n - x}} & \text{­­­(3)} \end{matrix}$

$\begin{matrix} \begin{array}{l} {Var\lbrack t\rbrack = A\left( {1 - A} \right) +} \\ {\left( {m - 1} \right)m \cdot \left( \begin{array}{l} n \\ {2x} \end{array} \right) \cdot \left( \frac{2}{m} \right)^{2x}\left( {1 - \frac{2}{m}} \right)^{n - 2x}\left( \begin{array}{l} {2x} \\ x \end{array} \right)\left( \frac{1}{2} \right)^{2x}} \end{array} & \text{­­­(4)} \end{matrix}$

where

$A = m \cdot \begin{pmatrix} n \\ x \end{pmatrix}\left( \frac{1}{m} \right)^{x}\left( {1 - \frac{1}{m}} \right)^{n - x},$

and the combination

$\begin{pmatrix} n \\ x \end{pmatrix} = \frac{n!}{x!\left( {n - x} \right)!}.$

The equations were experimentally validated by performing numerical simulations with 5000 independent runs for each simulated case. Complete agreement with the analytical solutions was observed.

Stochastic Labeling of Individual Molecules

Methods are disclosed herein that may be applied to determining small numbers of biological molecules and their changes in response to, for example, cellular response, differentiation or signal transduction. The methods may also be used in performing a wide variety of clinical measurements. Although many analytical methods have been developed to measure the relative abundance of different molecules through sampling (e.g., microarrays and sequencing), the methods disclosed herein are able to determine the absolute number of molecules in a sample.

Methods for performing single molecule digital counting by the stochastic labeling of a collection of identical molecules are disclosed. As illustrated in FIGS. 1, 2A and 2B, each copy of a molecule (from a collection of identical target molecules 103) randomly captures a label by choosing from a large, non-depleting reservoir of diverse labels 101. The uniqueness of each labeled molecule is governed by the statistics of random choice, and depends on the number of copies of identical molecules in the collection compared to the diversity of labels. Once the molecules are labeled each has been given a unique identity and can now be separately detected. In some aspects, it is preferable to first amplify the labeled targets prior to detection so that simple present/absent threshold detection methods can be used. Counting the number of labels is used to determine the original number of molecules in solution. In some aspects, the molecules to be counted are each members of a class that shares some common feature, for example, they may each be a single copy of a particular gene sequence or nucleic acid sequence. Counting may be applied, for example, to mRNA targets, splice products, alternatively spliced products, structural RNAs, tRNA, miRNA, siRNA, microRNA and the like. Similarly, counting may be applied to DNA, for example, gene copy number, chromosome number, mitochondrial DNA, bacterial genomes, pathogen nucleic acid, viral nucleic acids and the like. Counting may be applied in research of disease in humans or other mammals or agricultural organisms, e.g. cattle, chicken, wheat, rice, fish, etc. Counting may also be applied to counting aspects of microbes, such as environmental measurements, e.g. water quality testing. The methods may be particularly useful where small numbers of items are to be counted and an accurate count is desirable rather than a relative estimate.

One embodiment is illustrated schematically in FIG. 1 . The library of different label-tag sequences 101 is combined with a sample that includes an unknown number of targets of interest 103. Three different species of target are shown, 103 a, 103 b and 103 c, present at 4, 6 and 3 copies respectively. The individual label-tag oligonucleotides from library 101 are covalently attached to the different targets to form target-label-tag molecules 105. Each target has a collection of different label-tag molecules 105 a, 105 b and 105 c and within each target-specific collection the members differ in the label-tag oligo that is attached. On the array 107, each target is tiled in combination with all possible label-tag combinations represented with each different combination being present at a different known or determinable location on the array. In the figure each different possible combination of target and label-tag is represented by a single probe for illustration purposes, but on the array each different probe is preferably present in a feature having multiple copies of the same probe sequence. The array is divided into subarrays 107 a, 107 b and 107 c for illustrative purposes. The upper portion 109 of the probes varies at each feature according to the different label-tag. The lower portion 113 is the same for all features of each subarray and is complementary to the target. After hybridization individual features of the array are labeled through hybridization of the complementary target-label-tag molecule to the feature. The figure shows a detectable label 111 may be used to detect features where a target-label-tag is hybridized.

FIG. 2A illustrates the attachment of different labels from the pool 101 to each of 4 different copies of the same target “t”. Label 20 is attached to tl, label 107 to t2, label 477 to t3 and label 9 to t4. The labeled targets are then amplified to generate four unique populations, each population representing a single occurrence of the target in the starting sample.

FIG. 2B illustrates the method for a comparison of two samples, sample 1 and 2. The target 201 Gene A is present in 2 copies in sample 1 and 9 copies in sample 2. Both samples have non-target molecules 203. The labels 205 are combined with the samples and target molecules are attached to individual label-tag molecules in a stochastic manner. The targets with attached label-tags are hybridized to an array 211 having many features, there is a feature for each possible target-label-tag combination. Some of the features are labeled, for example, 209 and others are not, for example, 207. The labeled features indicate the presence of a specific target-label-tag combination and each corresponds to a count. As shown for gene A in sample 1 there are two labeled features so the count is 2. For Gene A in sample 2 there are 9 labeled features so the count is 9.

The stochastic labeling process can be generalized as follows for illustrative purposes. Consider a given target sequence defined as T = {t₁, t₂ .... tn}; where n is the number of copies of T. A set of labels is defined as L = {l₁, l₂ .... lm}; where m is the number of different labels. T reacts stochastically with L, such that each t becomes attached to one 1. If the l’s are in non-depleting excess, each t will choose one l randomly, and will take on a new identity l_(i)t_(j); where l_(i), is chosen from L and j is the j^(th) copy from the set of n molecules. We identify each new molecule l_(i)t_(j) by its label subscript and drop the subscript for the copies of T, because they are identical. The new collection of molecules becomes T* = l₁t + l₂t + .... l_(i)t; where l_(i), is the i^(th) choice from the set of m labels. It is important to emphasize that the subscripts of l at this point refer only to the i^(th) choice and provide no information about the identity of each 1. In fact, l₁ and l₂ will have some probability of being identical, depending upon the diversity m of the set of labels. Overall, T* will contain a set of k unique labels resulting from n targets choosing from the non-depleting reservoir of m labels. Or, T*(m,n) = {tl_(k)}; where k represents the number of unique labels that have been captured. In all cases, k will be smaller than m, approaching m only when n becomes very large. We can define the stochastic attachment of the set of labels on a target using a stochastic operator S with m members, acting upon a target population of n, such that S(m)T(n) = T*(m,n) generating the set {tl_(k)}. Furthermore, since S operates on all molecules randomly, it can independently act on many different target sequences. Hence, the method can simultaneously count copies of multiple target sequences. The distribution of outcomes generated by the number of trials n, from a diversity of m, can be approximated by the Poisson equation, P_(x) = ^(x)/x!e^(-(n/m)), P₀ is the probability that a label will not be chosen in n trials, and therefore, 1-P₀ is the probability that a label will occur at least once. It follows that the number of unique labels captured is given by k = m(1-P₀) = m(1 -e^(-(n/m))).

Given k, we can calculate n. In addition to using the Poisson approximation, the relationship for k, n and m can be described analytically using the binomial distribution, or simulated using a random number generator, each yielding similar results (see SOM).

The outcome of stochastic labeling is illustrated by examining the graph of k verses n (curve 3201 in FIG. 11 ) calculated using a label diversity (m) of 960. As expected, the number of unique labels captured depends on the ratio of molecules to labels, n/m. When n is much smaller than m, each molecule almost always captures a unique label, and counting k is equivalent to counting n. As n increases, k increases more slowly as given by eq. 1, and yet remains a very precise estimate of n. For example, when n/m is ~0.01, the ratio of unique labels to molecules k/n ~0.99, and we expect an increase of 10 molecules will generate 10 +/-X new labels. As n/m approaches 0.5 (i.e., ~480 molecules reacted with 960 labels), k/n ~0.79 and ~6 +/-X new labels are expected with an increase of 10 molecules. At high n/m, k increases more slowly as labels in the library are more likely to be captured more than once. Curve 3202 in FIG. 11 shows the number of labels chosen exactly once, and curve 3203 shows the number of labels chosen exactly twice as n increases. Curve 3201 shows the number of labels captured at least once. A more complete description of the number of times a label is chosen as a function of n is shown in FIG. 15 .

The methods and examples below demonstrate that a population of indistinguishable molecules can be stochastically expanded to a population of uniquely identifiable and countable molecules. High-sensitivity threshold detection of single molecules is demonstrated, and the process can be used to count both the absolute and relative number of molecules in a sample. The method should be well suited for determining the absolute number of multiple target molecules in a specified container, for example in high-sensitivity clinical assays, or for determining the number of transcripts in single cells. The approach should also be compatible with other molecular assay systems. For example, antibodies could be stochastically labeled with DNA fragments and those that bind antigen harvested. After amplification, the number of labels detected will reflect the original number of antigens in solutions. In the examples shown here, DNA is used because of the great diversity of sequences available, and because it is easily detectable. In principle, any molecular label could be used, for example fluorescent groups or mass spectroscopy tags, as long as they are easily detected and they have sufficient diversity for the desired application. Although many of the examples refer to populations.

It is instructive to contrast the attributes of stochastic labeling with other quantitative methods. Microarray and sequencing technologies are commonly used to obtain relative abundance of multiple targets in a sample. In the case of microarray analysis, intensity values reflect the relative amount of hybridization bound target and can be used to compare to the intensity of other targets in the sample. In the case of sequencing, the relative number of times a sequence is found is compared to the number of times other sequences are found. Although the techniques differ by using intensity in one case and a digital count in the other, they both provide relative comparisons of the number of molecules in solution. In order to obtain absolute numbers, quantitative capture of all sequences would need to be assured; however in practice the efficiency of capture with microarray and sequencing technologies is unknown.

Digital PCR is an absolute counting method where solutions are stochastically partitioned into multi-well containers until there is an average probability of one molecule per two containers, then detected by PCR(4). This condition is satisfied when, P₀ = (1 -e^(-n/c)) = ½; where n is the number of molecules and c is the number of containers, or n/c is 0.693. Quantitative partitioning is assumed, and the dynamic range is governed by the number of containers available for stochastic separation. Once the molecules are partitioned, high efficiency PCR detection gives the yes/no answer and absolute counting enabled. To vary dynamic range, micro-fabrication can be used to substantially increase the number of containers (5). Similarly, in stochastic labeling, the same statistical conditions are met when P₀ = (1 -e^(-n/m)) = ½; where m is the number of labels, and one half of the labels will be used at least once when n/m = 0.693. The dynamic range is governed by the number of labels used, and the number of labels can be easily increased to extend the dynamic range. The number of containers in digital PCR plays the same role as the number of labels in stochastic labeling and by substituting containers for labels we can write identical statistical equations. Using the principles of physical separation, digital PCR stochastically expands identical molecules into physical space, whereas the principle governing stochastic labeling is identity based and expands identical molecules into identity space.

New methods and compositions for single molecule counting employing the use of stochastic labeling are disclosed herein. In preferred aspects, a diverse set of labels is randomly attached to a population of identical molecules is converted into a population of distinct molecules suitable for threshold detection. Random attachment as used herein refers to a process whereby any label can be attached to a given molecule with the same probability. To demonstrate stochastic labeling methods experimentally the absolute and relative number of selected genes were determined after stochastically labeling 360,000 different fragments of the human genome. The approach does not require the physical separation of molecules and may take advantage of highly parallel methods such as microarray and sequencing technologies to simultaneously count absolute numbers of multiple targets. In some embodiments, stochastic labeling may be used for determining the absolute number of RNA or DNA molecules within single cells.

The methods disclosed herein may be used to take quantitative measurements of copies of identical molecules in a solution by transformation of the information to a digital process for detecting the presence of different labels. The stochastic properties of the method have been measured, and the relative and absolute digital counting of nucleic acid molecules is demonstrated. The method is extremely sensitive, quantitative, and can be multiplexed to high levels. In some aspects a microarray-based detection method is used, but the method is extendable to many other detection formats.

In some aspects, the methods are based on probability theory, where the outcome of chemical reactions occurring between a set of labeling molecules and a set of target molecules is modeled and tested. When all of the molecules in a uniform mixture of fixed volume collide and react randomly, the chemical events follow a stochastic process governed in part by the molecule concentration of each species (D. T. Gillespie, The Journal of Physical Chemistry 81, 2340 (1977)).

Methods for analyzing genomic information often utilize a correlation between a measurement of the amount of material associated with a location. The location can be, for example, a feature of an array that contains a specific sequence that is known or can be determined or any type of solid support such as a bead, particle, membrane, etc. A common aspect to these methods is often hybridization of a target to be measured to a complementary probe attached to the solid support. The probe may be, for example, an oligonucleotide of known or determinable sequence, but may also be BACs, PACs, or PCR amplicons.

Because of the density of different features that can be obtained using synthesis methods such as photolithography, microarrays can be applied to high density applications. For example, at feature sizes of 1 micron square an array can have about 10⁸ features per cm². Within a feature, depending on the chemistry used for synthesis, the probes are spaced typically at about 10 nm spacing resulting in about 10⁴ molecules in a micron². At approximately full saturation about 10% of those probes are hybridized with target. There are then about 640 functional molecules in an array having 1 micron² spacing between features (~800 nm² functional area). This relatively small number of functional molecules in a feature limits the dynamic range for estimating relative concentration from hybridization signal intensity.

Methods are disclosed herein to overcome the dynamic range limitations observed with small feature sizes and small numbers of molecules on the array surface, by using a counting or digital readout as a substitute for the typical analog signal resulting from array hybridization.

Methods that use signal intensity to estimate relative concentrations of targets typically label the targets with a detectable label, often after an amplification step, and through hybridization of the labeled target to the probe, the probe and thus the feature is also labeled. The amount of label is detected and correlated with a measurement of the amount of target in the sample. The estimate of amount of a given target in a sample is typically relative to other targets in the sample or to previously obtained measurements and may be based on comparison to targets present in the sample at known or expected levels or to controls within the sample. This type of analysis can and has been used successfully, for example, to estimate genomic copy number to detect copy number variation in individuals or in cell populations (see, for example, Pinkel & Albertson, Annu. Rev. Genomics Hum. Genet. 6, 331-354 (2005), Lucito et al. Genome Res. 13, 229102305 (2004), Sebat et al. Science 305, 525-528 (2004), Zhou et al., Nat. Biotechnol. 19, 78-81 (2001) and Zhao et al. Cancer Res. 65, 5561-5570 (2005) and U.S. Pat. Pub. Nos. 20040157243 and 20060035258) or to estimate gene expression levels (see, for example, Lockhart et al., Nat. Biotechnol. 14:1675-1680 (1996), and Wodicka et al., Nat. Biotechnol. 15:1359-1367 (1997)).

Correlating intensity of hybridization signal or signal intensity with concentration of target molecules has limitations and can typically provide only an estimate of the absolute amount of a target, and may not be an accurate count of the actual amount of target present. The estimate may be an under or over estimate, particularly when comparing different targets or different samples. This is the result of many different factors, including but not limited to, differences between probes, feature specific effects, sample specific effects, feature size (as it decreases the ability to correlate accurately decreases) and experimental variation. Much of this variation can be addressed by data analysis methods, but the methods do not provide counting of individual molecules or events and are therefore subject to estimation errors.

In preferred aspects methods are disclosed for attaching a different label-tag sequence to each molecule of a particular target sequence or more preferably a collection of target sequences of interest. For example, a sample having 100 molecules of target type 1 is mixed with an excess, for example, 1000 different label-tag sequences, forming a library of label-tag sequences under ligation conditions. Multiple copies of the library of label-tag sequences are added so there are preferably many copies of each label-tag. Different label-tag sequences from the library are appended to each of the 100 target molecules so that each of the 100 molecules of the first target sequence has a unique label-tag sequence appended thereto. This results in 100 different target-label-tag combinations. The target-label-tag molecules may then be amplified to enrich the target-label-tag products relative to other non-targets. Amplification after labeling alters the absolute amount of the target, but because each occurrence in the original sample has been uniquely labeled this will not alter the count. The amplified target-label-tag products, whether amplified or not, can then be labeled with a detectable label, and hybridized to an array of probes. The features of the array that have target-label-tag hybridized thereto can be detected, for example, by labeling the hybridization complex with a fluorescent label and detecting the presence of signal at the features. In this example, because there are 1000 different labels possible and a single target being analyzed, there are 1000 different possible label-target sequences that might be generated so an array having a different feature for each of the 1000 different possibilities can be used. Assuming each target is labeled and no label is used twice, 100 of the 1000 different features should be detectable, indicating the corresponding label has been used.

Consider 1 copy of a target molecule in solution identified as t1. React this target against a set of 10 labels, Lm = {l₁, l₂, ... l₁₀}. Each label has a 0.1 probability of being chosen. Next consider multiple copies of the target, t_(n), reacted against the set of L_(m) (assume non-depelting reservoir of labels). For simplicity, consider 3 copies of t: t₁, t₂ and t₃. Target t₁ will choose a label, t₂ has a 0.9 probability of choosing a different label, t₃ has a predictable probability of choosing the same label as t₁ or t₂. For n copies choosing from m labels, outcomes can be modeled by the binomial distribution as discussed above. For 3 targets and 10 labels, the probability of a label not being chosen, P₀ is (1-(⅒))³ = 0.729. The probability P₁ of being chosen exactly once is (3/10)(1-(⅒))² = 0.243. The probability of being chosen twice, P₂ is 0.027 and the probability P₃ of being chosen 3 times is 0.001. Since P₀ is the probability of not being chosen, 1-P₀ is the probability of being chosen at least once. We define k = m(1-P₀) as the number of labels we expect to see in an experiment. Conversely, if we know m, and observe k we can solve for the number of molecules. In the previous example where n=3 and m=10 we expect to see 10(1-P₀) or 2.71 labels as our most probable outcome. Increasing m dramatically increases our counting efficiency, accuracy and dynamic range, e.g. for m = 1,000, k(number of labels expected for n=10, k = 9.96, for n = 20, k = 19.8.

Once the target molecules are labeled with the counter they can be amplified freely without impacting the counting since the readout is either yes, indicating detection or no indication not detected. In one aspect, a simple detector having m elements for each target sequence can be constructed. The detector may be an array. An array having 10⁸ features or elements could assay 10⁵ different targets using 10³ different labels, for example. Other detection methods do not require individual elements for each counter, for example, sequencing.

In preferred aspects the “counter library” or “label-tag library” has approximately the same number of copies of each label-tag in the library. The label-tag sequences are not target specific, but are like the tags that have been used for other tagging applications, for example, the Affymetrix GENFLEX tag array. Preferably all label-tags in a set of label-tags will have similar hybridization characteristics so that the label-tags of the set can be detected under similar conditions.

For each target there are a series of features on the array, preferably one feature for each label-tag. In each of these features the portion of the probe that hybridizes to the target (or target complement) is the same but the label-tag complement is different in each feature. For example, to detect a first target RNA, “RNA1”, there would be a series of features each having a different probe (RNA1-tag1, RNA1-tag2...RNA1tagN). For each target to be detected there is a similar set of features, e.g. RNA2-tag1, RNA2-tag2, ...RNA2-tagN. The set of label-tags is N tags and it is the unique combination of the label-tag with the target sequence that creates a novel sequence to be detected, for example, by hybridization.

Label-tag attachment to individual targets is a stochastic process whereby the probability of any given label-tag being attached to any target is stochastic. There is a random selection of label-tags by attaching the label-tags to the end of a known target sequence in a sequence independent manner. The label-tag is attached without requirement for it to hybridize to any portion of the target so there is no or minimal bias as to which label-tag sequence is attached. Individual molecules all look the same for the purpose of attachment of the label-tag.

The label-tag may be attached to the target by any method available. In one embodiment, the label-tag is attached by ligation of the label-tag to one of the ends of the target. In preferred aspects the probes of the array are complementary to a predicted junction between target and label so it is preferable that the labels are attached to all occurrences of a target at the same position. This is facilitated if the termini of each occurrence of a selected target are the same and are known. In one aspect, target occurrences are fragmented with a restriction enzyme so that defined ends of known sequence are formed.

After label-tag attachment in some embodiments the target-label-tag segment is amplified. Attachment of universal primers to either end followed by PCR amplification is one method for amplifying. The universal primers may be added along with the label or at a subsequent ligation step.

For RNA targets an RNA ligase, such as T4 RNA ligase may be used. T4 RNA ligase 1 catalyses the ligation of a 5′ phosphryl-terminated nucleic acid donor to a 3′ hydroxyl-terminated nucleic acid acceptor. Substrates include single-stranded RNA and DNA. See, for example, Romaniuk, P. and Uhlenbeck, O. (1983) R. Wu, L. Grossman and K. Moldave (Eds.), Methods Enzymol., 100, pp. 52-56. New York: Academic Press and Moore, M.J. and Sharp, P.A. (1992) Science, 256, 992-997. RNA targets may also be circularized and used as template for rolling circle amplification using an enzyme having reverse transcriptase activity. T4 RNA ligase 1 may be used for circularization of RNA by ligating the ends of the molecule together. T4 RNA ligase 1 can also be used to ligated RNA to DNA.

Full-length mRNA can be selected by treating total or poly(A) RNA with calf intestinal phosphatase (CIP) to remove the 5′ phosphate from all molecules which contain free 5′ phosphates (e.g. ribosomal RNA, fragmented mRNA, tRNA and genomic DNA). Full-length mRNAs are not affected. The RNA can them be treated with tobacco acid pyrophosphatase (TAP) to remove the cap structure from the full-length mRNA leaving a 5′-monophosphate. A synthetic RNA adapter can be ligated to the RNA population. Only molecules containing a 5′-phosphate, (i.e. the uncapped, full-length mRNAs) will ligate to the adapters. Preferably the adapter has a variable label sequence, and may also have a constant sequence for priming. Preferably, the constant sequence is 5′ of the variable sequence. In some aspects, the adapter ligated mRNA may then be copied to form a first strand cDNA by, for example, random priming or priming using oligo dT. The cDNA may subsequently be amplified by, for example, PCR.

T4 RNA ligase may also be used for ligation of a DNA oligo to single stranded DNA. See, for example, Troutt et al., (1992) Proc. Natl, Acad. Sci. USA, 89, 9823-9825.

In other aspects, the ligated target-label-tag molecule may be enriched in the sample relative to other nucleic acids or other molecules. This enrichment may be, for example, by preferentially amplifying the target-label-tag methods, using for example, a DNA or RNA polymerase, or by degrading non target-label-tag molecules preferentially.

In one aspect, the target-label-tag molecule may be nuclease resistant while the unligated target and unligated label molecules may be nuclease sensitive. A nuclease can be added to the sample after ligation so that ligated target-label-tag molecules are not digested but non-ligated molecules are digested. For example, the targets may be resistant to a 5′ exonuclease (but not a 3′ exonuclease) while the labels are resistant to a 3′ exonuclease but not a 5′ exonuclease. Ligating target to label generates a molecule that is resistant to 5′ and 3′ exonuclease activity. After ligation the sample may be treated with a 5′ exonuclease activity, a 3′ exonuclease activity or both 5′ and 3′ exonuclease activities. For examples of nucleases see Rittie and Perbal, J. Cell Commun. Signal. (2008) 2:25-45, which is incorporated by reference (in particular see Table 5). Exo VII, for example degrades single stranded DNA from both the 5′ and 3′ ends so the sample could be treated with Exo VII after ligation to degrade molecules that are not ligation products.

In another aspect amplification may include a rolling circle amplification (RCA) step. See for example, Baner et al. (1998) NAR 26:5073, Lizardi et al. (1998) Nat. Genet. 19:225, Fire and Xu, (1995) PNAS 92:4641-5, Zhao et al. Angew Chem Int Ed Engl. 2008; 47:6330-6337 and Nilsson et al. (2008), Trends in Biotechnology, 24:83-88. The targets may be ligated so that they have a label and a universal priming (UP) sequence attached to the 5′ end of the targets. The UP-label-target is then ligated to form a circle. A primer complementary to the UP is then hybridized to the circles and extended using a strand displacing polymerase. The resulting amplification product contains multiple copies of the complement of the circle, UP-target-L.

In another aspect, targets may be labeled in a copying step. For example, a primer having a 3′ target specific region and a 5′ variable label region may be hybridized to the targets, either RNA or DNA, and extended to create a single complimentary copy of the target. Each extension product will have a different label and the junction between the label and the target specific region is known. The extension may be performed in the presence of nuclease resistant nucleotides so that the extension product is resistant to nuclease but the unextended primers are not. After extension the reaction is treated with a 3′-5′ exonuclease activity to digest unextended primer. Exonuclease I, for example, removes nucleotides from single stranded DNA in the 3′ to 5′ direction and Exo III removes nucleotides from the 3′ termini of duplex DNA. Exonuclease T (or RNase T) is a single-stranded RNA or DNA specific nuclease that requires a free 3′ terminus and removes nucleotides in the 3′ to 5′ direction. The extension products are then detected by hybridization to probes that are complementary to the primers and include the unique label portion and the constant target specific portion. If the target is RNA it can be digested with RNase H after extension. The extension product may also be amplified before hybridization.

In some aspects the probability that any two targets are labeled with the same label may be decreased by using two or more labeling steps. For example, a first labeling step where each target has a label selected from a set of labels followed by a second labeling set using the same set of labels. The first labeling event will be independent of the second so the probability that the first and second labeling events will both be the same in two independent targets is the product of the probability of two targets having the same label in either step. If there are N possible labels, and the first target is labeled first with label N1 and then with label N4, the probability that a second target will be labeled also with N1 and then N4 is 1/N2. So if there are 100 different labels, the probability that two targets will be labeled with the same label in the first round and the same label in the second round is 1/10,000.

In another aspect a first round of labeling may be done with 16 probes (for example, all possible 2 base combinations) and then a second round of labeling is done using the same 16 probes. The chance of any one probe attaching to a given target occurrence in the first round is 1 out of 16, the chance that the same probe will attach to the second target is 1/16 and the chance that the same two probes will attach is 1/16 X 1/16 or 1/256.

In another aspect reversible terminators are used to add a sequence to the end of each target being counted. For example, a 6 base sequence may be added and the chance of two being the same is 1 in 46 or 1 in 4096. See, for example, WO 93/06121 and US 6140493 which disclose stochastic methods for synthesizing random oligomers.

There is a finite set of labels, L_(1-x) and each target to be detected is present in the sample at a certain integer occurrence (T1_(1-t) ¹, T2 _(1-t) ², ...TN_(1-t) ^(n)). In a preferred aspect, the method is used to count the number of each of the different targets, (e.g. how many occurrences of T1, how many of T2,...how many of TN) in the sample. The targets are independently labeled with the label molecules. Labeling is stochastic, so that any given target occurrence can be labeled with any one of the labels. For example, T1-1/L689, T1-2/L3, T1-3/L4,567 and so on. For Target 2, any given occurrence can also be labeled with any of the label molecules. This might generate, for example, (T2-1, L5), (T2-2, L198), (T2-3, L34) and so on. There are multiple copies of each label so T2-1 might be labeled with L5 and T1-500 may also be labeled with L5.

The methods disclosed herein may be used to measure random cell-to-cell variations in gene expression within an isogenic population of cells. Such variation can lead to transitions between alternative states for individual cells. For example, cell-to-cell variation in the expression of comK in B. subtilis has been shown to select cells for transition to the competent state in which genes encoding for DNA uptake proteins are expressed. See, Maamar et al. Science 317:526-529 (2007) which is incorporated herein by reference.

In some aspects the labels are generated within the target to be counted. For example, the label may be a unique cleavage site in a target fragment as shown in FIG. 6 . Each of the copies of the target to be counted 601 have a common sequence at one end identified in the figure as 603. This may be a common sequence that has been added to the targets through ligation or primer extension or it may be a naturally occurring sequence in the target. The targets are fragmented randomly, for example by shearing or sonnication resulting in cleavage at the points indicated by the arrows to generate cleavage products 604. Cleavage is at a different and unique site in each of the fragments and results in a unique sequence in the target immediately to the left of the point of cleavage in the illustration (indicated by circles in fragments 607). This unique sequence can function as a label for the disclosed methods. A second common sequence 605 may be attached to each of the targets immediately downstream of the cleavage point, through for example ligation of an adaptor sequence. The resulting targets 607 can be analyzed directly to determine how many unique sequences are present and using this number as an indication of the number of targets in the starting sample. This is illustrated for nucleic acids, but could similarly be applied to proteins or other contiguous strings of monomers or units that are assembled in a non repeating pattern.

FIG. 7 shows a strategy for selecting probes for target fragments. For a double stranded fragment there are 4 possible junctions that can be targeted with array probes 3001, 3003, 3005 and 3007. Each of these junction regions as shown has a counter region 3011 denoted by N’s, a fixed sequence 3013 that is defined by the restriction enzyme used for fragmentation and a target specific region 3015. The region 3015 is shown as N’s but in preferred aspects it is a known and predictable sequence of the target that is adjacent to the selected restriction site. In a preferred aspect, the array probes are complementary to at least a portion of 3011, a portion of 3015 and all of 3013. For each target sequence-counter combination there are 4 different probes that could be included on the array. For example, if the targets are 10 loci from each of 4 chromosomes and 4 probes per fragment are included for 1200 different labels (1000 specific plus 200 non-specific) the array would have 192,000 total probes (4 × 10 × 4 × 1200).

In some aspects methods for selecting a collection of labels optimized for use in the disclosed methods is contemplated. For example, a list of all possible 14 mers may be used as a starting pool (4¹⁴ is ~268 million different sequences). Different label lengths can be used resulting in different numbers of starting sequences. Eliminate all labels that are not at least 50% GC content. Eliminate all labels that do not use each of the 4 possible nucleotides at least twice. Eliminate all labels that have more than two Gs or Cs in tandem, e.g. a probe with GGG or CCC would be eliminated, or with more than three As or Ts in tandem, e.g. AAAA or TTTT would be removed. Remove labels that contain a selected restriction site. Remove labels having a Tm that is outside of the range (38.5 to 39.5° C.). In other embodiments the range may be about 38 to 40, 38-39, or 39-40. Remove probes that have self complementarity beyond a selected threshold. Perform a hierarchical clustering to maximize sequence differences between labels to minimize cross hybridization, same label to same probe. Minimize self-complementarity within the collection to reduce tendency of two labels binding to each other.

FIG. 8 shows a counter adaptor 3101 that includes a counter region 3103, a constant region for priming 3105 and a sticky end 3107 for ligation to an overhang created by restriction digestion, for example with BamHI. After ligation of the adaptors 3101 to the target fragment 3109 there are two adaptors ligated to the target fragment, one at either end. It is probable that the counters on the two ends will be different although there is a predictable probability of having the same counter ligated to both ends of the same fragment. After adaptor ligation the fragment 3111 can be amplified by PCR using a common primer to the 3103 region of the adaptor. The adaptor may first be filled in to make it double stranded. The PCR amplification may be used to preferentially amplify fragments of a selected size range, for example, 300 to 2 kb. Smaller fragments are not amplified as efficiently because of self complementarity between the ends of the individual strands (capable of forming a panhandle structure that inhibits amplification) and longer fragments (longer than about 3 kb) also don’t amplify well.

After circularization, the uncircularized fragments can be digested using an exonuclease, for example. The circularized fragments can be amplified using target specific primers to generate amplification product 3113. In the figure the target specific primers are identified as TS primer F and TS primer R. Whereas the primers used to amplify 3111 are common to all adaptor ligated fragments and will amplify all fragments that are in the size range to be amplified using PCR, the TS primers are specific for selected targets to be analyzed. The amplification product 3113 has in the 5′ to 3′ direction, target specific sequence, overhang sequence, a first counter, first adaptor sequence, circularization junction 3115, second adaptor sequence, second counter, second overhang sequence and a second target specific sequence. The first and second counter are different (although they may be the same at a low probability) and the first and second target sequence are different. The product 3113 or preferably fragments thereof can be detected by a variety of methods, for example, an array of probes as exemplified by probe 3117 can be used. The array probe 3117 is complementary to a region of the target, the overhang region and the counter. When hybridized the target will have an overhanging single stranded region that corresponds to the adaptor sequence. A labeled probe 3119 that is complementary to one strand of the adaptor can be hybridized and the ligated to the array probe as shown, and as described below.

FIG. 9 shows a method for reading out the labeled targets on arrays. On the left, the target with G₁ ligated to L₁, “G₁L₁”, is shown hybridizing to the complementary array probe over the entire length of the probe. On the right target G₁ ligated to label L₂ is shown partially hybridized to the G₁L₁ probe on the array. On the left the biotin labeled constant segment can hybridize to the G₁L₁ target and ligate to the 5′ end of the G₁L₁ array probe. The constant segment can hybridize to the L₂ segment but will not ligate to L₁. This allows for labeling of properly hybridized target-label pairs with both hybridization and ligation discrimination. The lower panel shows an example where the target or G portion is not matching with the probe on the array. This will not ligate efficiently because it hybridizes less stably.

The left panel shows the results when target G₁ ligated to label L₁ to form G₁L₁ hybridizes to the complementary G₁L₁ probe on the array. The constant region (in white) can hybridize to its labeled complement so that the 3′ end of the labeled complement is juxtaposed with the 5′ end of the L₁ region of the probe on the array and the ends can be ligated. In the center panel the target hybridizing to the G₁L₁ probe is non-cognate, the label region is L₂ and not L₁ so it does not hybridize to the L₁ region of the probe. The labeled oligo can hybridize to the partially hybridized target but it is not juxtaposed with the 5′ end of the L₁ region of the probe so it should not ligate to the probe. In the right panel the target shown hybridized has the L₁ region and is complementary to the array probe at that region, but the array probe has a G region that is not G₁ so the G₁L₁ target does not hybridize. The labeled oligo can hybridize to the target but because the L1:L1 region is short the duplex is not stable and the labeled oligo does not ligate to the end of the array probe.

If you have N targets T (T₁, T₂,...T_(N)) and each is present at a number of copies C (C₁, C₂, ...C_(x)) where X varies from target to target (X_(T1), X_(T2), ...X_(TN)) and you ligate to a set of Y different labels (L₁, L₂, ...L_(Y)) then you generate, for example, T₁C₁L₁, T₁C₂L₂, ...T_(N)C_(x)L_(XT1), where X <<<Y). So, for example, if T1 is gene A and T2 is gene B and gene A is present in the sample at 500 copies and gene B is present at 100 copies, each copy of gene A, 1 to 500, will be attached to a different label (so there will be -500 different labels attached to the gene A copies), and each copy of gene B, 1 to 100, will be attached to a different label.

A method for counting the number of occurrences of each of a plurality of same targets in a mixture of targets comprising multiple occurrences of each type of a plurality of different targets. In preferred aspects, the mixture of targets is a nucleic acid sample that contains different amounts of multiple target sequences. For example, there may be target sequences 1, 2, 3, 4 and 5 that are expression products from 5 different genes, occur in the sample as follows: 1000 copies of target 1, 100 copies of target 2, 500 copies of target 3, 10 copies of target 4 and 50 copies of target 5. The targets are preferably of known sequence and are treated so that they may be ligated to a label-tag sequence.

FIG. 1 shows one embodiment of the method. Labels or counters 101 are combined with assay targets 103 so that each target is combined with one label to form label-targets 105. The process of combining an individual target with individual label molecules is a stochastic process. The number of labels each target type combines with is directly proportional to the number of individual targets of that target type or the copy number of the target. The number of labels is counted by hybridization to arrays where individual label-targets are detected at different features.

The targets are mixed with a collection of label-tag sequences, each label-tag being a different sequence and the collection having a number that is preferably 10 times the number of copies of the most abundant target to be counted. In a preferred aspect, the label-tags are a collection of known sequences such as a collection of all possible 6mers (N₆). Each of the label-tag sequences is present in multiple copies in the mixture, but all are present at approximately equal amounts. The label-tag sequences are ligated to the targets. Ligation is random so that any given label-tag has about the same probability of ligating to any one target occurrence. So if there are 1000 different targets each could be ligated to a different label-tag sequence and the probability that any two target occurrences will have the same label-tag ligated is low. Because the ligation is a random stochastic process there is a known probability that if there are C copies of a given target and N different label-tags that any two copies of a target T will have the same label.

T1, T2, ...TN. C1, C2,...CX, L1, L2,...LY where T are the different targets and there are N different targets, C are the different copies of a target and there are X copies of that target and L are the different label label-tags and there are Y label tags. X varies for each target and determining X is one of the objects of the present invention. The relationship between X and Y determines the probability that two C’s will have the same L. In preferred aspects Y is greater than X for each target to be counted. This reduces the probability of undercounting due to double labeling. If C1 and C2 of T1 are both labeled with L3 both copies will be counted as a single occurrence, resulting in under counting. Undercounting can also be adjusted for by estimating the number of copies that are likely to be multiply labeled and adjusting the final count upwards to take those into account. For example, if there is a likelihood that 5 of 1000 copies will be labeled with the same label tag then the final number should be adjusted up by 0.5%.

In preferred aspects, the detection is by hybridization to an array of probes. The array has a collection of features for each target that includes a different feature for each label tag. For example, if there are X label tags there are X features for each target, T1L1, T1L2,...T1LX and the same for target 2, T2L1, T2L2,...T2LX, out to TNL1, TNL2, ...TNLX. The number of features of the array is on the order of X times N. Each probe has a target complementary sequence and a label tag complementary sequence. Within a set of probes for a given target the target segment of the probe would remain constant and the label tag portion varies from feature to feature so that each label tag sequence is represented by at least one feature for each target.

In one aspect, the methods may be used to count the number of copies of each of a plurality of targets in a sample. The amount of target containing sample mixed with the label tags may be diluted so that the number of copies of each target to be counted is less than the number of label tags. For example, if the targets to be counted are present at about 1,000 copies per cell and there are 10,000 label tags you want to have the amount of sample in the mixture to be about the equivalent of one cell’s worth of RNA. You can mix that with multiple copies of each label-tag, but you want to keep the absolute number of copies of target below the number of types of label tag sequences. Dilution of the sample and use of an appropriately small amount of starting material may be used. If a target sequence is present at low copy number per cell it is possible to use the nucleic acid from a larger number of cells. For example, to measure the DNA copy number of a chromosomal region relative to other chromosomal regions the expected copy number is low (e.g. 2 for normal) so if there are 10,000 different label tags, the number of genomes that can be added to the sample for attachment of label tags can be high, e.g. 500 to 1000.

In one aspect, the methods are used to identify regions of genomic amplification and chromosomal abnormalities. For example, the methods may be used to detect trisomy. Most of the chromosomal regions will be present in 2 copies per cell and the region of trisomy will be present in 3 copies per cell. You would expect to observe a 3:2 ratio in your count. For example, if you have 500 genomes you would have 1000 copies of most regions and 1500 copies of the trisomy regions. Small errors in the counting, resulting from undercounting, would have little or no effect on the counting.

In some aspects, controls of known copy number may be spiked in to a sample to determine accuracy.

Stochastic labeling of t_(1,N) (collection of essential identical molecules of copy 1, 2....N of target 1) by L_(1,m) (effectively an infinite reservoir of diversity m when m is much greater than N) . This allows for complete or near complete resolution of members of t1,N, by imparting separate identities to the members of the collection of t_(1,N) (provided that M is sufficiently smaller than N in the labeling). This provides for a stochastic or random projection of t_(1,N) onto L_(1,m). In some aspects L_(1,m) is a library and the members of the library that are associated with t_(1,N) can be counted to determine the number of copies of the target. In some aspects the methods can be described as indexing the members of the target. This provides a method to follow individual molecules that are members of a type of molecule that would not otherwise be distinguishable one from another.

Because stochastic labeling can impart identifiability to otherwise non-identifiable molecules it can impart identifiability to any two targets that may be very similar, but different. Examples of targets that may be highly similar but could be separately counted using the disclosed methods, include, for example, alternative splice forms of a gene, and sequences that have one or more variations, including a variation in a single base (e.g. SNP or indels (insertion or deletions of short regions, e.g. 1-5 bases). In some aspects the methods impart a clonal labeling, that allows a single copy to be separately detected and separately isolated from the solution.

Some nucleic acid sequencing reactions use methods that stochastically attach targets to a solid support followed by amplification of the attached target and analysis. The target attaches in an unknown location and the location can be determined by sequencing the amplified target at specific locations. In contrast, the disclosed methods provide for clonal amplification of known targets in a known location. The stochastic nature of the formation of the target-label-tag molecule provides a mechanism for isolating single occurrences of selected targets that can be subsequently amplified and analyzed. In some aspects the label can be used as a handle for isolating clonal populations of targets. The labeling step generates an indexed library that has a variety of applications. For example, the indexed library could be used for sequencing applications. The method adds distinguishability to any set of molecules, even molecules that are not distinguishable by other mechanisms because they may share common regions or even been identical. The indexed library can be stored and used multiple times to generate samples for analysis. Some applications include, for example, genotyping polymorphisms, studying RNA processing, and selecting clonal representatives to do sequencing.

In some aspects the methods are used to stochastically label a polyclonal antibody population. This may be used to identify different polyclonal populations.

The methods may be used to convert an analog readout of hybridization signal intensities on arrays into a measurable process that can be scored digitally on the arrays. The method leverages a random process where the tagging of assayed molecules is governed by stochastic behavior. In a random process, the more copies of a given target, the greater the probability of being tagged with multiple labels. A count of the number of incorporated labels for each target can approximate the abundance level of a given target of interest. The ability to count labels on microarrays would be a clear cost-advantage over the other existing techniques.

Serial analysis of gene expression (SAGE) is another method for analysis of gene expression patterns. SAGE relies on short sequence tags (10-14 bp) within transcripts as an indicator of the presence of a given transcript. The tags are separated from the rest of the RNA and collected. The tags can be linked together to form long serial molecules that can be cloned and sequenced. Quantitation of the number of times a particular tag is observed provides an estimate of the relative expression level of the corresponding transcript, relative to other tagged transcripts. See, for example, Velculescu et al. Science 270, 484-487 (1995) and Velculescu et al. Cell 88 (1997). Again this method provides a relative estimate of the abundance of a transcript and not an actual count of the number of times that transcript appears. Other methods based on counting and estimating relative abundance have also been described. See, for example, Wang et al. Nat. Rev. Genet. 10, 57-63 (2009). Additional methods for digital profiling are disclosed, for example, in U.S. Pat. Pub. 20050250147 and US 7,537,897.

A stochastic counting assay system as described herein can also be a sub-system within a much larger bio-analysis system. The bio-analysis system could include all the aspects of sample preparation prior to, for example, optical detection, the post processing of data collected in the optical detection phase and finally decision making based on these results. Sample preparation may include steps such as: extraction of the sample from the tested subject (human, animal, plant environment etc.); separation of different parts of the sample to achieve higher concentration and purity of the molecules under investigation; sample amplification (e.g. through PCR); attachment of fluorescence tags or markers to different parts of the sample; and transfer of the sample or a portion of the sample into a reaction vessel or site on a substrate. The post processing of the collected data may include: normalization; background and noise reduction; and statistical analysis such as averaging over repeated tests or correlation between different tests. The decision making may include: testing against a predefined set of rules and comparison to information stored in external data-bases.

The applications and uses of the stochastic labeling and counting methods and systems described herein can produce one or more result useful to diagnose a disease state of an individual, for example, a patient. In one embodiment, a method of diagnosing a disease comprises reviewing or analyzing data relating to the presence and/or the concentration level of a target in a sample. A conclusion based review or analysis of the data can be provided to a patient, a health care provider or a health care manager. In one embodiment the conclusion is based on the review or analysis of data regarding a disease diagnosis. It is envisioned that in another embodiment that providing a conclusion to a patient, a health care provider or a health care manager includes transmission of the data over a network.

Accordingly, business methods relating to the stochastic labeling and counting methods and methods related to use thereof as described herein are provided. One aspect of the invention is a business method comprising screening patient test samples for the amount of a biologically active analyte present in the sample to produce data regarding the analyte, collecting the analyte data, providing the analyte data to a patient, a health care provider or a health care manager for making a conclusion based on review or analysis of the data regarding a disease diagnosis or prognosis or to determine a treatment regimen. In one embodiment the conclusion is provided to a patient, a health care provider or a health care manager includes transmission of the data over a network.

Applications for the disclosed methods include diagnosing a cancerous condition or diagnosing viral, bacterial, and other pathological or nonpathological infections, as described in U.S. Pat. No. 5,800,992. Additional applications of the disclosed methods and systems include, pathogens detection and classification; chemical/biological warfare real-time detection; chemical concentration control; dangerous substance (e.g., gas, liquid) detection and alarm; sugar and insulin levels detection in diabetic patients; pregnancy testing; detection of viral and bacterial infectious diseases (e.g. AIDS, Bird Flu, SARS, West Nile virus); environmental pollution monitoring (e.g., water, air); and quality control in food processing.

Any available mechanism for detection of the labels may be used. While many of the embodiments discussed above use an array readout form, it will be obvious to one of skill in the art that other methods for readout may be used. For example, sequencing may be preferred in some embodiments.

In some aspects the readout is on an array. The array may be a solid support having immobilized nucleic acid probes attached to the surface in an ordered arrangement. The probes may be, for example, synthesized in situ on the support in known locations using photolithography or the probes may be spotted onto the support in an array format. As discussed above, in some embodiments the array includes a probe feature for each possible label-target combination. A feature preferably includes many copies of a single probe sequence. The feature may also have some probes that are not full length, resulting from truncation of synthesis. The photo activation process may not be 100% efficient so some probes are terminated at each step without having subsequent bases added. These truncated probes have the sequence of a portion of the full length probe.

Sequencing readout. After attachment of the labels to the targets in a stochastic manner, the targets may be amplified according to any of the methods disclosed herein and the amplification product may be subjected to any available sequencing method.

A number of alternative sequencing techniques have been developed and many are available commercially. For a review see, for example, Ansorge New Biotechnology 25(4):195-203 (2009), which is incorporated herein by reference. These include the use of microarrays of genetic material that can be manipulated so as to permit parallel detection of the ordering of nucleotides in a multitude of fragments of genetic material. The arrays typically include many sites formed or disposed on a substrate. Additional materials, typically single nucleotides or strands of nucleotides (oligonucleotides) are introduced and permitted or encouraged to bind to the template of genetic material to be sequenced, thereby selectively marking the template in a sequence dependent manner. Sequence information may then be gathered by imaging the sites. In certain current techniques, for example, each nucleotide type is tagged with a fluorescent tag or dye that permits analysis of the nucleotide attached at a particular site to be determined by analysis of image data.

In another aspect, mass spec analysis may be used to detect the labels and count the targets. The labels can be distinguishable based on size or other property that can be detected. Many of the examples provided herein identify the label based on unique nucleic acid sequence but any distinguishable label may be used, for example, the pool of labels may be labels that are differentially detectable based on fluorescence emission at a unique wavelength.

FIG. 9 shows a method for reading out the labeled targets on arrays. On the left, the target with G₁ ligated to L₁, “G₁L₁”, is shown hybridizing to the complementary array probe over the entire length of the probe. On the right target G₁ ligated to label L₂ is shown partially hybridized to the G₁L₁ probe on the array. On the left the biotin labeled constant segment can hybridize to the G₁L₁ target and ligate to the 5′ end of the G₁L₁ array probe. The constant segment can hybridize to the L₂ segment but will not ligate to L₁. This allows for labeling of properly hybridized target-label pairs with both hybridization and ligation discrimination. The lower panel shows an example where the target or G portion is not matching with the probe on the array. This will not ligate efficiently because it hybridizes less stably.

The left panel shows the results when target G₁ ligated to label L₁ to form G₁L₁ hybridizes to the complementary G₁L₁ probe on the array. The constant region (in white) can hybridize to its labeled complement so that the 3′ end of the labeled complement is juxtaposed with the 5′ end of the L₁ region of the probe on the array and the ends can be ligated. In the center panel the target hybridizing to the G₁L₁ probe is non-cognate, the label region is L₂ and not L₁ so it does not hybridize to the L₁ region of the probe. The labeled oligo can hybridize to the partially hybridized target but it is not juxtaposed with the 5′ end of the L₁ region of the probe so it should not ligate to the probe. In the right panel the target shown hybridized has the L₁ region and is complementary to the array probe at that region, but the array probe has a G region that is not G₁ so the G₁L₁ target does not hybridize. The labeled oligo can hybridize to the target but because the Ll:L1 region is short the duplex is not stable and the labeled oligo does not ligate to the end of the array probe.

The methods are broadly applicable to counting a population of molecules by performing a stochastic operation on the population to generate a stochastic population of identifiable molecules. The targets need not be identical. For example, the methods may be used to count the absolute number of members of a group. In one aspect, a sample having an unknown number of copies of a selected nucleic acid target is fragmented randomly so that on average each copy of the target has a different end resulting from a distinct fragmentation event. A common adaptor sequence can be ligated to the end of each fragment and used for amplification of the fragments. Each ligation event generates a new molecule having a junction formed by the end of the random fragment and the adaptor sequence. The new junction can be detected by, for example, sequencing using a primer complementary to the adaptor or a region of the adaptor. Because the fragmentation was a stochastic process the number of different ends detected is a count of the number of different starting target molecules, assuming one fragment per starting target molecule.

The examples provided herein demonstrate the concept of using a stochastic labeling strategy in the high sensitivity detection and counting of individual DNA molecules. The difficult task of quantifying single nucleic acid molecules is converted into a simple qualitative assay that leverages the statistics of random probability; and at the same time, the requirement of single molecule detection sensitivity is achieved with PCR for the robust amplification of single DNA molecules. In some aspects improved methods for amplification will be used. For example, linear amplification methods may be used to mitigate the representation distortions created by exponential cycling in PCR. Given the lack of available techniques for single molecule counting, and the increasing need for its use, the new concept of stochastic labeling is likely to find numerous applications in the near future.

EXAMPLES

To demonstrate stochastic labeling, we performed an experiment to count small numbers of nucleic acid molecules in solution. Genomic DNA from a male individual with Trisomy 21 was used to determine the absolute and relative number of DNA copies of chromosomes X, 4 and 21, representing 1, 2 and 3 target copies of each chromosome, respectively. Genomic DNA isolated from cultured B-Lymphocytes of a male caucasion with Trisomy 21 was purchased from The Coriell Institute for Medical Research (Catalog # GM01921). The DNA quantity was determined by PICOGREEN dye (Invitrogen) measurements using the lambda phage DNA provided in the kit as reference standard. DNA quality was assessed by agarose gel electrophoresis.

The DNA concentration in the stock solution was measured by quantitative staining with picogreen fluorescent dye, and dilutions containing 3.62 ng, 1.45 ng, 0.36 ng and 0.036 ng were prepared. In each dilution, the number of copies of target molecules in the sample was calculated from a total DNA mass of 3.5 pg per haploid nucleus (see, T. R. Gregory et al., Nucleic Acids Res 35, D332 (2007), and represent approximately 500, 200, 50 and 5 haploid genomes. The absolute quantity of DNA in the sample was determined by optical density measurements and quantitative staining with PICOGREEN fluorescent dye (Invitrogen) prior to making dilutions.

As outlined in FIG. 3 , the genomic DNA sample 1901 was first digested to completion with the BamHI restriction endonuclease to produce 360,679 DNA fragments 1905. A diverse set of labels consisting of 960 14-nucleotide sequences was synthesized as adaptors harboring BamHI overhangs (SEQ ID Nos. 44-1963). Genomic DNA was digested to completion with BamHI (New England BioLabs, NEB) and ligated to a pool of adaptors consisting of an equal concentration of 960 distinct labels. Each adaptor consists of a universal PCR priming site, a 14 nucleotide long counter sequence and a BamHI overhang (similar to the form of the adaptor shown in FIG. 7 ). The sequence of the label adaptors SEQ ID Nos. 44-1963 were selected from an all-possible 414 nucleotide combination to be of similar melting temperature, minimal self-complementation, and maximal differences between one-another. Homopolymer runs and the sequence of the BamHI restriction site were avoided. Each pair, for example, SEQ ID Nos. 44 and 45, form an adaptor pair that has a region of complementarity starting at base 12 in SEQ ID No. 44 and base 5 in SEQ ID No. 45:

SEQ ID 44 5'CGACAGACGCCTGATCTTTTGTTAGCCGGAGT 3'

3'ACTAGAAAACAATCGGCCTCACTAG5'SEQID 45

The adaptors have a 5′ overhang of 11 bases in the even numbered SEQ IDs and 4 bases (GATC) in the odd numbered SEQ IDs. Oligonucleotides were synthesized (Integrated DNA Technologies) and annealed to form double-stranded adaptors prior to pooling. For ligation, the digested DNA was diluted to the desired quantity and added to 100 pmoles (equivalent to 6 x 1013 molecules) of pooled label-adaptors, and 2x106 units (equivalent to 1 × 1013 molecules) of T4 DNA ligase (NEB) in a 30 µl reaction. The reaction was incubated at 20° C. for 3 hours until inactivation at 65° C. for 20 minutes.

For the stochastic labeling reaction, each DNA fragment-end randomly attaches to a single label by means of enzymatic ligation of compatible cohesive DNA ends to generate labeled fragments 1907. High coupling efficiency is achieved through incubation with a large molar excess of labels and DNA ligase enzyme (~1013 molecules each). At this stage, the labeling process is complete, and the samples can be amplified as desired for detection. A universal primer may be added added, and the entire population of labeled DNA fragments may be PCR amplified. The PCR reaction preferentially amplifies approximately 80,000 fragments in the 150 bp-2 kb size range (FIG. 21 ). Adaptor-ligated fragments were amplified in a 50 µl reaction containing 1X TITANIUM Taq PCR buffer (Clontech), 1 M betaine (Sigma-Aldrich), 0.3 mM dNTPs, 4 µM PCR004StuA primer (SEQ ID No. 1974), 2.5U Taq DNA Polymerase (USB), and 1X TITANIUM Taq DNA polymerase (Clontech). An initial PCR extension was performed with 5 minutes at 72° C.; 3 minutes at 94° C.; followed by 5 cycles of 94° C. for 30 seconds, 45° C. for 45 seconds and 68° C. for 15 seconds. This was followed by 25 cycles of 94° C. for 30 seconds, 60° C. for 45 seconds and 68° C. for 15 seconds and a final extension step of 7 minutes at 68° C. PCR products were assessed with agarose gel electrophoresis and purified using the QIAQUICK PCR purification kit (Qiagen).

The purified PCR product was denatured at 95° C. for 3 minutes prior to phosphorylation with T4 polynucleotide kinase (NEB). The phosphorylated DNA was ethanol precipitated and circularized using the CIRCLIGASE II ssDNA Ligase Kit (Epicentre). Circularization was performed at 60° C. for 2 hours followed by 80° C. inactivation for 10 minutes in a 40 µl reaction consisting of 1X CIRCLIGASE II reaction buffer, 2.5 mM MnCl2, 1 M betaine, and 200U CIRCLIGASE II ssDNA ligase. Uncirculated DNAs were removed by treatment with 20U Exonuclease I (Epicentre) at 37° C. for 30 minutes. Remaining DNA was purified with ethanol precipitation and quantified with OD260 measurement.

Amplification of gene targets. Three assay regions were tested: One on each of chromosomes 4, 21 and X. The genomic location (fragment starting and ending positions are provided), of the selected fragments are as follows: Chr4 106415806_106416680 (SEQ ID No. 1), Chr2l 38298439_38299372 (SEQ ID No. 2), and ChrX 133694723_133695365 (SEQ ID No. 3). The lengths are 875, 934 and 643 bases respectively. The circularized DNA was amplified with gene specific primers (SEQ ID Nos. 4-9) in a multiplex inverse PCR reaction. PCR primers were picked using Primer3 (available from the FRODO web site hosted by MIT) to yield amplicons ranging between 121 and 168 bp. PCR was carried out with 1X TITANIUM Taq PCR buffer (Clontech), 0.3 mM dNTPs, 0.4 µM each primer, 1X TITANIUM Taq DNA Polymerase (Clontech), and ~200 ng of the circularized DNA. After denaturation at 94° C. for 2 minutes, reactions were cycled 30 times as follows: 94° C. for 20 seconds, 60° C. for 20 seconds, and 68° C. for 20 seconds, with a 68° C. final hold for 4 minutes. PCR products were assessed on a 4-20% gradient polyacrylamide gel (Invitrogen) and precipitated with ethanol.

The amplified DNA was fragmented with DNase I, end-labeled with Biotin, and hybridized to a whole-genome tiling array which spans the entire non-repetitive portion of the genome with uniform coverage at an average probe spacing of ~200 nt (see Matsuzaki et al., Genome Biol 10, R125 (2009) and Wagner et al. Systematic Biology 43, 250(1994)). Probe intensity (“Array Intensity”) from the whole-genome tiling array (y-axis) is grouped into 200 nt bins by the length of the BamHI fragment on which it resides. High probe intensity demonstrates the amplification of fragments in the 600 bp ~ 1.2 kb size range (x-axis, log-scale). The computed size distribution of BamHI restricted fragments in the reference genome sequence (NCBI Build 36) is shown by the curve labeled “Number of Fragments”. After circularization of the amplified products to obtain circles 1909, three test target fragments were isolated using gene-specific PCR; one on each of chromosomes X, 4, and 21, and prepared for detection.

The three labeled targets were counted using two sampling techniques: DNA microarrays and next-generation sequencing. For the array counting, a custom DNA array detector capable of distinguishing the set of labels bound to the targets was constructed by dedicating one array element for each of the 960 target-label combinations. Each array element consists of a complementary target sequence adjacent to one of the complements of the 960 label sequences (as shown in FIG. 3 ).

Array Design: For each gene target assayed, the array probes tiled consist of all possible combinations of the 960 counter sequences connected to the two BamHI genomic fragment ends (FIG. 8 ). An additional 192 counter sequences that were not included in the adaptor pool were also tiled to serve as non-specific controls. This tiling strategy enables counter detection separately at each paired end, since each target fragment is ligated to two independent counters (one on either end).

Arrays were synthesized following standard Affymetrix GENECHIP manufacturing methods utilizing lithography and phosphoramidite nucleoside monomers bearing photolabile 5′-protecting groups. Array probes were synthesized with 5′ phosphate ends to allow for ligation. Fused-silica wafer substrates were prepared by standard methods with trialkoxy aminosilane as previously described in Fodor et al., Science 251:767 (1991). After the final lithographic exposure step, the wafer was deprotected in an ethanolic amine solution for a total of 8 hrs prior to dicing and packaging.

Hybridization to Arrays: PCR products were digested with Stu I (NEB), and treated with Lambda exonuclease (USB). 5 µg of the digested DNA was hybridized to a GeneChip array in 112.5 µl of hybridization solution containing 80 µg denatured Herring sperm DNA (Promega), 25% formamide, 2.5 pM biotin-labeled gridding oligo, and 70 µl hybridization buffer (4.8 M TMACl, 15 mM Tris pH 8, and 0.015% Triton X-100). Hybridizations were carried out in ovens for 16 hours at 50° C. with rotation at 30 rpm. Following hybridization, arrays were washed in 0.2X SSPE containing 0.005% Trition X-100 for 30 minutes at 37° C., and with TE (10 mM Tris, 1 mM EDTA, pH 8) for 15 minutes at 37° C. A short biotin-labeled oligonucleotide (see 3119 in FIG. 8 ) was annealed to the hybridized DNAs, and ligated to the array probes with E.coli DNA ligase (USB). Excess unligated oligonucleotides were removed with TE wash for 10 minutes at 50° C. The arrays were stained with Streptavidin, R-phycoerythrin conjugate (Invitrogen) and scanned on the GCS3000 instrument (Affymetrix).

In order to maximize the specificity of target-label hybridization and scoring, we employed a ligation labeling procedure on the captured sequences (FIG. 8 ). We set thresholds to best separate the intensity data from the array into two clusters, one of low intensity and one of high intensity to classify labels as either being used or not (FIGS. 22, 23 and 29 ). We score a label as “present” and counted if its signal intensity exceeded the threshold. To count labels we set thresholds for the array intensity, or the number of sequencing reads. Appropriate thresholds were straightforward to determine when used and un-used labels fall into two distinct clusters separated by a significant gap. In situations where a gap was not obvious, the function normalmixEM in the R package mixtools was used to classify labels. This function uses the Expectation Maximization (EM) algorithm to fit the data by mixtures of two normal distributions iteratively. The two normal distributions correspond to the two clusters to be identified. The cluster of labels with a high value is counted as “used”, and the other as “not used”. The average of the minimum and maximum of the two clusters, (I_(min) + I_(max))/2, was applied as the threshold for separating the two clusters.

Sampling error calculation. A sampling error can be introduced when preparing dilutions of the stock DNA solution. This error is a direct consequence of random fluctuations in the number of molecules in the volume of solution sampled. For example, when exactly 10 µl of a 100 µl solution containing 100 molecules is measured, the actual number of molecules in the sampled aliquot may not be exactly 10. The lower the concentration of the molecules in the entire solution, the higher the sampling error, and the more likely the actual abundance in the sampled aliquot will deviate from the expected abundance (n = 10). To calculate sampling errors, we determined the number of molecules for each chromosome target in our stock DNA solution and performed numerical simulations to follow our dilution steps in preparing the test samples (3.62 ng, 1.45 ng, 0.36 ng and 0.036 ng). To illustrate, if the dilution step is sampling 1 µl of a 25 µl solution containing 250 molecules, we create 25 bins and randomly assign each of the 250 molecules into one of the bins. We randomly choose one bin and count the number of molecules assigned to that bin to simulate the process of sampling 1/25th of the entire solution. If a serial dilution was performed, we would repeat the simulation process accordingly. For each dilution, the observed copy number ratios of Chr 4:X or 21:X for 10,000 independent trials are summarized as observed medians, along with the 10^(th) and 90^(th) percentiles and shown in FIGS. 12 and 13 .

As an alternate form of detection, the samples were submitted to two independent DNA sequencing runs (FIG. 10 ). The arrangement and position of the adaptors and PCR primers used to convert the DNA sample hybridized to microarrays into sequencing templates are shown in the figure. The circularized junction 3115 is located between the two counter labels. PCR primers that have restriction sites are used to amplify two fragments. The fragments are digested with the restriction enzymes to generate ends compatible with ligation to sequencing adaptors. The sequencing adaptors are ligated to the ends to generate a fragment that has the label sequence and a portion of the target that is 48 to 94 base pairs in length are flanked by sequences for use with SOLID sequencing.

Validation by DNA sequencing (First SOLID run). DNA targets that were used for hybridization to arrays were converted to libraries for sequencing on the SOLID instrument (ABI). P1 and P2 SOLID amplification primers were added to the DNA ends through adaptor ligation and strand extension from gene-specific primers flanked by P1 or P2 sequences (FIG. 10 ). Each sample received a unique ligation adaptor harboring a 4-base encoder (SEQ ID Nos. 34-43) that unambiguously identifies the originating sample of any resulting read. Each adaptor includes two strands, SEQ ID Nos. 34 and 35, 36 and 37, 38 and 39, 40 and 41 or 42 and 43, that hybridize to form a double stranded region of 29 base pairs and a single stranded 4 base overhang (GATC). Individual libraries were prepared for each sample, and quantified with picogreen before equal amounts of each sample was combined into a single pooled library. DNA sequencing was performed on SOLID v3 by Cofactor Genomics. A total of ~46 million 50 base reads were generated. Each read is composed of three segments, corresponding to the sample encoder, label sequence and gene fragment (FIG. 10 ). We removed reads if: uncalled color bases were present, the average Quality Value (aQV) of the whole read < 10, the aQV of the sample encoder < 20, or the aQV of the label sequence < 18. 40% of the raw reads were removed. Filtered reads were mapped to reference sequences using the program Short Oligonucleotide Color Space (SOCS), available from ABI with a maximum tolerance of 4 color mismatches between the first 45 color bases in each read and reference sequences (the last 5 color bases on 3′ end of each read were trimmed in alignment). About 64.3% reads were uniquely mapped to reference sequences, of which 89.5% (16 million) have high mapping quality, i.e., with no mismatch in the sample encoder and at most 1 mismatch in the label sequence. These high-quality reads, accounting for ~35% of the total reads generated, were used in subsequent counting analysis.

Sequencing replication (Second SOLID run). An aliquot of the exact same DNA library originally sequenced by Cofactor Genomics was subsequently resequenced by Beckman Coulter Genomics. Approximately 50 million 35 base reads were generated, and processed following the same rules. Approximately 61% of the raw reads passed quality filters, of which 81% uniquely mapped to a reference sequence with a maximum tolerance of 3 color mismatches (An adjusted mismatch tolerance was applied in the alignment step to account for the shorter length of these reads). Of the mapped reads, 91% (22.5 million) are of high mapping quality, i.e., with perfect match in the sample encoder and at most 1 mismatch in the label sequence. These high-quality reads (45% of the total raw reads generated) were used for counting analysis.

Between several hundred thousand to several million reads were used to score the captured labels. Table 1 shows the number of mapped reads from SOLID DNA sequencing.

TABLE 1 DNA sample 5 ng 2 ng 0.5 ng 0.05 ng 0 ng Chr4 Left side 1st SOLiD run 709,076 252,211 237,380 316,629 1,204 2nd SOLiD run 621,372 73,962 189,937 237,520 411 Right side 1st SOLiD run 1,724,955 1,662,958 1,114,246 2,201,078 3,353 2nd SOLiD run 1,422,673 1,359,512 839,775 980,616 2,386 Chr21 Left side 1st SOLiD run 1,615,416 1,474,208 832,234 1,428,540 1,851 2nd SOLiD run 1,296,685 1,038,456 622,429 930,461 840 Right side 1st SOLiD run 1,124,772 886,421 551,192 849,204 821 2nd SOLiD run 910,298 522,358 367,207 479,621 224 ChrX Left side 1st SOLiD run 444,960 316,975 254,386 515,213 744 2nd SOLiD run 266,606 157,860 137,706 220,121 5 Right side 1st SOLiD run 1,227,047 921,214 777,033 1,064,531 64 2nd SOLiD run 1,043,475 768,296 559,038 695,873 43

We set thresholds for the number of sequencing reads observed for each label, and score a label as “present” and counted if the number of sequencing reads exceeded the threshold. Label usage summaries from experimental observations or from the stochastic modeling are shown in Table 2. The number of attached labels, k, detected for each target in each dilution either by microarray counting or sequence counting is presented in Table 2, and plotted in FIGS. 4 and 5 .

Several dilutions (3.62 ng, 1.45 ng, 0.36 ng and 0.036 ng) of DNA isolated from cultured of a Trisomy 21 male individual were processed for microarray hybridization (FIG. 12 left) and DNA sequencing (FIG. 12 right). Three gene targets were tested from chromosome X, 4 and 21, and observed numbers of detected labels are shown (“observed”). The number of target molecules for each sample was determined from the amount of DNA used, assuming a single haploid nucleus corresponds to 3.5 pg. For comparison, the calculated number of labels expected to appear using a stochastic model are also plotted (“calculated”). Numerical values are provided in Table 4. Relative copy ratios of the three gene targets (FIG. 13 ): ChrX (right bar), Chr4 (left bar) and Chr2l (center bar) representing one, two and three copies per cell, respectively. Different dilutions (3.62 ng, 1.45 ng, 0.36 ng and 0.036 ng) of the DNA isolated from cultured lymphoblasts of a Trisomy 21 male individual were processed for microarray hybridization and DNA sequencing. The calculated number of target molecules was determined from the number of labels detected on microarrays (Table 4, column 9) or from the SOLiD sequencing data. For each sample dilution, the copy number ratio of each gene target relative to ChrX is shown for Microarray (FIG. 13 left) and SOLiD sequencing (FIG. 13 right). For comparison, relative copy ratios obtained from in silico sampling simulations are also shown in (FIG. 13 left) and (FIG. 13 right), where circles indicate the median values from 10,000 independent trials and error bars indicate the 10th and 90th percentiles. The 90th percentile values of the relative copy ratios at the lowest concentration (0.036 ng) are explicitly labeled in the plots.

TABLE 2 DNA sample 3.62 ng 1.45 ng 0.36 ng 0.036 ng 0 ng Chr4 Stochastic Model 633 336 98 10 0 Left side Microarray 501 260 102 14 0 1st SOLiD run 513 251 101 14 0 2nd SOLiD run 516 273 102 14 0 Right side Array 525 256 107 14 0 1st SOLiD run 544 291 103 13 1 2nd SOLiD run 557 307 103 13 1 Chr21 Stochastic Model 769 457 143 15 0 Left side Microarray 651 335 160 20 0 1st SOLiD run 678 381 152 20 0 2nd SOLiD run 665 358 161 18 0 Right Microarray 627 341 157 20 0 side 1st SOLiD run 650 381 146 19 0 2nd SOLiD run 653 379 146 19 0 ChrX Stochastic Model 400 186 50 5 0 Left side Microarray 281 148 50 11 0 1st SOLiD run 290 149 43 11 0 2nd SOLiD run 300 150 45 11 0 Right side Microarray 306 133 48 10 1 1st SOLiD run 336 153 50 12 0 2nd SOLiD run 344 167 43 11 0

The counting results span a range of approximately 1,500 to 5 molecules, and it is useful to consider the results in two counting regimes, below and above 200 molecules. There is a striking agreement between the experimentally observed number of molecules and that expected from dilution in the first regime where the ratio of molecules to labels (n/m) < 0.2 (Table 2). Below 200 molecules the data are in tight agreement, including the data from the lowest number of molecules, 5, 10 and 15 where the counting results are all within the expected sampling error for the experiment (The sampling error for 10 molecules is estimated to be 10 ± 6.4, where 10 and 6.4 are the mean and two standard deviations from 10,000 independent simulation trials).

In the second regime above 200 molecules, there is an approximate 10-25% undercounting of molecules, increasing as the number of molecules increases. We attribute this deviation to be due to a distortion in the amplification reaction. PCR-introduced distortion occurs from small amounts of any complex template due to the differences in amplification efficiency between individual templates (2, 3). In the present case, stochastic labeling will produce only one (at low n/m ratios), and increasingly several copies (at higher n/m ratios) of each template. Modeling suggests that simple random dropout of sequences (PCR efficiencies under 100%) generate significant distortion in the final numbers of each molecule after amplification. At any labeling ratio, random dropout of sequences due to PCR efficiency will result in an undercount of the original number of molecules. At high n/m ratios, the number of labels residing on multiple targets will increase and have a statistical survival advantage through the PCR reaction causing greater distortion. In support of this argument, we observe a wide range of intensities on the microarray and a wide range in the number of occurrences of specific sequences in the sequencing experiments (FIGS. 23, 29 ). This effect can be reduced by carrying out the reaction at n/m ratios near or less than 0.2, increasing the number of labels m, further optimization of the amplification reaction, or by employing a linear amplification method. Other factors, such as errors from inaccurate pipetting, could also contribute.

The lymphoblast cell line used in this study provides an internal control for the relative measurement of copy number for genes residing on chromosomes X, 4 and 21. FIG. 13 presents the relative number of molecules from all three chromosomes normalized to copy number 1 for the X chromosome. As shown, the measurements above 50 molecules all yield highly precise relative copy number values. At low numbers of molecules (0.036 ng), uncertainty results because the stochastic variation of molecules captured by sampling an aliquot for dilution are significant. Numerical simulations were performed to estimate the sampling variation, and summarized medians, along with the 10^(th) and 90^(th) percentiles of the copy number ratios and are shown in FIGS. 12 and 13 as circles and range bars, respectively. At the most extreme dilutions, where ~5, 10, and 15 molecules are expected for the chromosome X, 4 and 21 genes, the copy number ratios fall within the expected sampling error.

Overall, the identity of labels detected on the microarrays and in sequencing are in good agreement, with only a small subset of labels unique to each process (Table 7). Despite a high sequencing sampling depth (Table 1), a small number of labels with high microarray intensity appear to be missing or under-represented in the sequencing results. In contrast, labels that appear in high numbers in the sequencing reaction always correlate with high microarray intensities. No trivial explanation could be found for the labels that are missing from any given sequencing experiment. While under-represented in some experiments, the same labels appear as present with high sequence counts in other experiments, suggesting that the sequences are compatible with the sequencing reactions.

PCR validation. We used PCR as an independent method to investigate isolated cases of disagreement, and demonstrated that the labels were present in the samples used for the sequencing runs.

PCR was used to detect the presence of 16 label sequences (Table 3) which were either observed as high or low hybridization intensity on microarrays, and observed with either high or low numbers of mapped reads in SOLID sequencing. The Chr4 gene target was PCR amplified with 3 dilutions (0.1 pg, 1 pg, and 10 pg) of the 3.62 ng NA01921 sample, using the DNA target that was hybridized to microarrays, or the prepared SOLID library template. PCR products were resolved on 4% agarose gels and fluorescent DNA bands were detected after ethidium bromide staining

TABLE 3 Label ID Label Sequence 1st SOLiD reads 2nd SOLiD reads Microarray intensity Microarray target template SOLiD library template 112 AGATCTTGTGTCCG 0 2 15,907 1 2 182 ATCTTCGACACTGG 0 1 10,304 3 4 779 TCGAGATGGTGTTC 0 4 9,411 5 6 782 TCGGATAGAGAGCA 0 0 6,716 7 8 783 TCGGTACCAACAAC 1 4 13,132 9 10 290 CCAAGGTTTGGTGA 1 17 10,777 11 12 780 TCGCAAGAGGTAAG 1 1 8,915 13 14 570 GGAGTTACGGCTTT 1 2 8,252 15 16 741 TCAACCAGTAAGCC 794 400 466 17* 18* 424 CTGTAAACAACGCC 1,191 1,292 527 19* 20* 242 CACGATAGTTTGCC 905 781 1,103 21* 22 859 TGTACTAACACGCC 920 892 1,107 23* 24* 83 ACGCTAACTCCTTG 8,629 7,704 19,500 25 26 383 CGTTTACGATGTGG 7,278 6,402 19,022 27 28 804 TCTTAGGAAACGCC 0 0 70 29* 30* 834 TGCAATAGACGACC 0 1 72 31* 32*

Table 3. PCR detection for the presence of label sequences in the processed DNA sample that was hybridized to microarray, or in the DNA sequencing library. Each PCR contained 0.1 pg of template, which represents approximately 1 × 106 DNA molecules. The number of mapped sequencing reads and the microarray intensity of each of the 16 labels for this selected gene target (Chr4, 3.62 ng) are listed. The last 2 columns show the gel lane number containing the indicated sample. Those numbers indicated by an * correspond to reactions where PCR failed to detect the label sequence in the sample.

Although we can clearly confirm their presence in the sequencing libraries, it is unclear as to why these labels are missing or under-represented in the final sequencing data.

To test the stochastic behavior of label selection, we pooled the results of multiple reactions at low target concentrations (0.36 and 0.036 ng), where the probability that a label will be chosen more than once is small.

FIG. 14 shows that the number of times each label is used closely follows modeling for 1,064 data points obtained from microarray counting. The graph is a comparison between experimentally observed label usage rates (microarray results) with those predicted from stochastic model (stochastic model). At low target molecule numbers, the chance of multiple target ligations to the same label sequence is low. It is therefore reasonable to consider data from experiments with low target numbers (0.036 ng and 0.36 ng of DNA), from those experiments, a total of 1,064 labels were observed, with the total frequency of label usage ranging from 0 to 6. The theoretically expected label usage frequency for 1,064 target molecules was obtained by performing 5000 simulation runs, with multiple independent reactions simulated in each run. The error bars indicate one standard deviation from the corresponding means.

Furthermore, since each end of a target sequence chooses a label independently, we can compare the likely hood of the same label occurring on both ends of a target at high copy numbers. Table 4 columns 10-11 present the experimentally observed frequency of labels occurring in common across both ends of a target and their expected frequency from numerical simulations. No evidence of non-stochastic behavior was observed in this data.

TABLE 4 Gene target Genomic DNA amount (ng) Estimated # of molecules at either end Expected # of labels at either end Expected # of labels in common across paired-ends Microarray observed # of labels # of molecules inferred from microarray observed # of labels Expected # of labels in common across paired-ends Microarray observed # of labels in common across paired-ends L R Avg Chr4 3.62 1034 633 417.68 ± 11.35 501 525 513 733 273.96 ± 10.24 303 1.45 414 336 117.92 ± 7.83 260 256 258 300 69.22 ± 6.43 63 0.36 103 98 9.93 ± 2.81 102 107 104 110 11.26 ± 2.99 20 0.036 10 10 0.11 ± 0.32 14 14 14 14 0.20 ± 0.44 0 0 0 0 0 0 0 0 0 0 0 Chr21 3.62 1551 769 616.74 ± 11.94 651 627 639 1051 425.28 ± 11.37 453 1.45 620 457 217.36 ± 9.51 335 341 338 416 118.79 ± 7.83 130 0.36 155 143 21.37 ± 3.98 160 157 158 172 25.86 ± 4.38 32 0.036 15 15 0.24 ± 0.48 20 20 20 20 0.40 ± 0.62 0 0 0 0 0 0 0 0 0 0 0 ChrX 3.62 517 400 166.63 ± 8.81 281 306 294 351 90.14 ± 7.08 103 1.45 207 186 36.26 ± 4.98 148 133 140 151 20.34 ± 3.94 23 0.36 51 50 2.58 ± 1.52 50 48 49 50 2.45 ± 1.51 4 0.036 5 5 0.03 ± 0.16 11 10 10 10 0.10 ± 0.31 2 0 0 0 0 0 1 0 0 0 0 1 2 3 4 5 6 7 8 9 10 11

Labels detected on microarray experiments are quantified in Table 4. Indicated quantities (col. 2) of genomic DNA derived from a Trisomy 21 male sample were tested on 3 chromosome targets (col. 1). The estimated number of copies of target molecules (or haploid genome equivalents, col. 3), the number of labels expected by the stochastic model (col. 4), and the actual number of labels detected on microarrays (col. 6-8) are summarized. Because each gene target fragment paired-end consists of random, independent label ligation events at the left (L) and the right (R) termini, the number of identical labels expected (col. 5) can be predicted from computer simulations, and compared to the number actually detected (col. 11). Given the number of labels detected (col. 8), we obtain the corresponding number of copies of target molecules (col. 9) in our stochastic model, and the predicted occurrences of identical labels across paired-ends (col. 10). The numbers in col. 5 and 10 are the means from 5,000 independent simulation runs along with one standard deviation of the corresponding means, given the number of labels at either end (col. 4 and col. 9).

The detailed column information for Table 4 is as follows: column 1: name of tested gene targets; column 2: estimated number of target molecules at either left or right end, this number is determined by PICOGREEN dye measurement (Molecular Probes, Inc.), the DNA concentration is also listed in this column; column 3: number of labels expected to be observed/used at either end (predicted by theoretical models), given the estimated number of target molecules in 2nd column; column 4: number of labels expected to be observed in common across the paired-ends (predicted by theoretical models), given the estimated number of target molecules in 2nd column; column 5: empirically observed number of labels used at the left end of gene target; column 6: empirically observed number of labels used at the right end of gene target; column 7: empirically observed number of labels used in common across the paired-ends; column 8: number of target molecules predicted by theoretical models, based on the empirically observed number of labels used (i.e., number in 7th column); column 9: number of labels expected to be observed in common across the paired-ends, given the number of target molecules in 8th column; column 10: empirically observed number of labels that were used in common across the paired-ends of the gene target.

Example X: An array was designed having 48 target sequences. Each target was paired with one of 3840 labels or “counters” for a total of 48 x 3840 or 184,320 probes. The probes were 30 mers (30 nucleotides in length) and the assay was designed to test whether or not the 30 mer imparts sufficient discrimination. Of the 30 bases, 15 bases are from the labels and the other 15 bases are derived from the targets. The probes were assayed to determine if each label-target combination hybridizes specifically. A phage RNA ligase was used to join labels with targets. Universal priming sites of 18 bases were included on the 5′ end of the labels and the 3′ end of the targets, facilitating PCR amplification of the joined label-targets. The method is diagramed in FIG. 3 .

The 3840 distinct label oligos (counters) were single stranded oligos pooled from the Dde1 TACL primer panel (40 primer plates by 96 wells per plate for 3840 different oligos). An example label oligo 301 is shown

(SEQ ID NO: 1964) 5'TCGATGGTTTGGCGCGCCGGTAGTTTGAAC CATCCAT-3'.

The 48 different primers used as “targets” were synthesized using as target 48 different 21 nucleotide sequences from the Affymetrix TrueTag 5K_A array. An example target oligo 307 is shown

(SEQ ID NO: 1965) 5'GCCATTTACAAACTAGGTATTAATCGATCC TGCATGCC-3'.

The “label” or “counter” oligo has an 18 nt common sequence at the 5′ end and a 15-28 nt “label” (or “counter”) sequence at the 3′ end. An example “label” 305 is shown. The universal primer 303 common to all or a group of the label oligos has sequence 5′ TCGATGGTTTGGCGCGCC-3′ (SEQ ID NO: 1966) at the 5′ end and each target oligonucleotide has common sequence 311 5′ AATCGATCCTGCATGCCA-3′ (SEQ ID NO: 1967) at the 3′ end as universal priming sequence. The target oligos vary in sequence at the 5′ ends 309.

A 1:1 dilution of each of the 3840 counters was mixed with various dilutions of each of the 48 target oligos to simulate different expression levels under ligation conditions so that the 5′ end of the target oligos can be ligated to the 3′ end of the label oligos. In preferred aspects T4 RNA ligase may be used to join the ends of the single stranded oligos. The 5′ and 3′ ends of the target oligos are phosphorylated and the 5′ and 3′ ends of the label oligos are hydroxylated. After the ligation the products are amplified by PCR using primers to the universal priming sequences. Only those fragments that have both universal priming sequences 303 and 311 will amplify efficiently.

Each of the 48 target sequences may be tiled with each of the 3,840 counters, resulting in a total number of features on array = 48 x 3,840 = 184,320. This is the number of different possible combinations of target with label. The product of the ligation and amplification reactions is hybridized to the array. For each target, the number of features that light up is determined and can be compared to the known copy number of each target in the input sample.

To test the digital counting methods, also referred to as stochastic labeling a collection of label-tag sequences was provided. Each has a common 5′ universal priming sequence, preferably 15-20 bases in length to facilitate amplification, and a 3′ label sequence, preferably 17-21 bases in length. Each type of primer in the collection has the same universal priming sequence but each type has a label sequence that is different from all of the other types in the collection. In one aspect there are about 4,000 to 5,000 different types of label sequences in the collection to be used. For testing the method, a set of 50 target sequences was synthesized. The target sequences each have a universal priming sequence at the 3′ end (5′GCTAGGGCTAATATC-3′SEQ ID NO: 1968, was used in this experiment). Each of the 50 oligo target sequences that were generated has a different 21 base sequence from the GENFLEX array collection of sequences, for example, 5′ GCCATTTACAAACTAGGTATT′3′ SEQ ID NO: 1970. The collection of label-tag oligos and the collection of target oligos was mixed. Various dilutions of the different targets were used in the mixture of targets to simulate a mixed population present at different levels, for example, different expression or copy number levels. T4 RNA ligase was added to ligate the label-tag oligos to the target oligos. There are 5000 different types of label oligos and 50 different types of target oligos so the majority of the target oligos of the same type will be labeled with a type of label oligo that is different from all of the other target oligos of that type. So target oligo type 1, occurrence 1 will be labeled with a label oligo type A (11A) and target oligo type 1, occurrence 2, will be labeled with a different label oligo, label oligo type B (12B). There is a finite and calculable probability that two or more occurrences of the same target type will be labeled with the same label oligo (11A and 12A), but that probability decreases as the number of different types of label oligos increases relative to the number of occurrences of any given type of target.

The ligated target/label oligos are then amplified using primers to the universal priming sites. Labels can be incorporated during amplification. The labeled amplification product is then hybridized to an array. For each different possible combination of target (50) and label (5000) there is a different probe on the array that targets that junction of the target ligated to the label. There will therefore be 50 X 5000 different probes on the array or 250,000 different probes.

Scanned images of the 48x3840 array were analyzed and compared to expected results. A total of 8 of the 48 targets were ligated to a pool of 3840 labels (counters). The assay was as shown in FIG. 3 . The conditions were single strand deoxyoligonucleotide ligation using a phage RNA ligase to join the labels with targets. Universal priming sites on the targets and labels were included to enable PCR amplification of the joined label-targets. The ligation conditions were essentially as described in (Tessier, D.C. et al. (1986) Anal Biochem. 158, 171-178, 50 mM Tris-HCl, pH 8, 10 mM MgCl2; 10 ug/mL BSA, 25% PEG, 1 mM HCC, 20 uM ATP; 5:1 acceptor (labels) to donor (the 8 targets) ratio at 25 C overnight. The products were amplified using PCR, purified, biotin labeled with TdT, hybridized to the array, washed, stained, and scanned. The expected 8 blocks show hybridization to the array in the expected patterns.

Different ligation conditions were also tested by ligating either a single target or a pool of 48 targets to the 3,840 counters. The concentrations of the targets used in the experiment were high as in the previous experiment so most counters will be ligated to targets. In ligation 1 a single target was ligated to 3,840 labels. In ligation 2, 48 targets at 1:1 copy number were ligated to 3,840 labels. Ligation 3 is a negative control for PCR so no DNA was added. PCR with the pair of universal primers was performed using the ligation products as template and the products separated on a gel. As expected a band was observed from ligations 1 and 2, but not 3. The PCR products were labeled and hybridized to the array and the scan images after array hybridization were analyzed. As expected no signal was observed for ligation 3, all of the targets were observed for ligation 2 and the single expected target was observed for ligation 1.The single target lights up in the correct region of the chip, but background signal was also observed in unexpected locations. Increased stringency of hybridization conditions can be used to minimize hybridization to unexpected probes of the array.

In another example, conditions for optimization of hybridization to decrease cross hybridization were tested. The products used were as described above and hybridization was performed with formamide and with or without non-specific competitor (herring sperm DNA). The non-specific signal is significantly decreased in the presence of formamide, with and without non specific competitor. This demonstrates that even though the targets and counters alone have 15 bases of complementarity to probes on the array, the combination of target plus counter and the resulting increase to 30 bases of complementarity to the probes, results in specific hybridization. Within the block of 3,480 probes, there is heterogeneity in the hybridization intensity. Preliminary sequence analysis shows a strong correlation of GC content with high signals. To minimize this array probes may be selected to have similar melting temps for the counters or the target-counter combination may be optimized to obtain similar hybridization stabilities. For example, if two targets are to be analyzed the portions of each target that are to be part of the probe may be selected to have similar TMs.

To test the efficiency of T4 RNA ligase in the ligation of labels to targets, DNA ligase from E. coli was tested. This required a slight modification of the sample prep (as depicted in FIG. 7 ) by creating an overhang site for duplex ligation. The target in this example has a double stranded target specific portion and a single stranded overhang. The overhang may be, for example, a run of inosine bases, for example 6 to 9, or a string of random bases, for example, N6-16. DNA ligase is used to close the gap and generate a ligated product that includes the target strand and a label/counter from the pool of 3,840 counters. The PCR is carried out in the same manner as above using common primers.

The expected targets were observed, but some non-specific bands were also detected in the amplified DNA, even in the absence of the target. This suggests that the some of the 3,840 labels are combining with each other when this method is used. Selection of an optimized pool of labels may be used to mitigate such interference.

In another example random primed PCR was tested. Instead of a ligation step, the targets have a 3′ random region, that can be, for example, a degenerate region or an inosine region. The labels hybridize to the random region and the random region is used as a primer for extension through the label during the PCR step to append a copy of the label and the universal priming site at the 5′ end of the label oligo to the 3′ end of the target. The extended target has a copy of the label sequence and the universal priming sequence and can be amplified by PCR.

In another example, a purification method for removing excess unligated counters was tested. The method is shown schematically in FIG. 11 . The counters 101 and the targets 2103 are ligated to form counter-target molecules as shown previously. A support bound probe that is complementary to the universal primer at the end of the target oligonucleotides 2105, is used to separate counter-targets and targets from un-ligated counters. The support 2109 may be, for example, a magnetic bead. A second separation can be used to separate counter-targets from un-ligated targets. The second separation uses a support bound probe complementary to the universal priming sequence at the end of the counters 2107. The single capture reduces background amplification. A double round of capture may also be used.

In FIG. 18 a scatter plot is shown to illustrate one way of representing the combinations of different target occurrences ligated randomly to different labels in the set. The plot shows combinations for 20 different target occurrences (labeled 1 to 20) representing 20 copies of the same target. The Y-axis represents different labels identified by a number from 1 to 1000. Each of the targets can be labeled with any of the 1000 labels, for example target 1 is labeled with label 351 and has coordinates (1, 351). The labels are distinct and distinguishable while the targets are the same in this example.

FIG. 19 shows a schematic where genomic DNA 1901 is fragmented, for example at restriction sites 1903 to produce fragments 1905. The fragments are ligated with labels to form fragments labeled at both ends 1907. All fragments can be ligated to the labels The label-ligated fragments are circularized, for example, by ligation of the label ends to form closed circles 1909 with first and second labels forming a single label 1911. The circularized fragments can be treated with exonuclease to remove unligated fragments. The circle and label can be amplified using gene-specific PCR primers 1913. The PCR product has the label region 1911 flanked by target specific regions. The array probe is preferably complementary to the junction between the target specific region and the label. There are two such junctions 1915 and 1917 in the PCR product and each could be targeted on either strand (since the product is double stranded). The products may be fragmented, labeled and hybridized to an array of probes to the junctions. The label-target combination can be hybridized to an array for counting.

FIG. 20 shows a graph of counting efficiency on Y axis and copies of target on X axis. The different lines represent different numbers of labels being used, from 1000 to 10,000. The inset graph is a blow up of the upper left hand region of the larger graph and shows how counting efficiency changes with the number of labels. Fewer labels results in a more rapid decrease in counting efficiency as the number of targets increases.

FIG. 21 is a plot of labels observed per target as the copies of targets increases and the number of label types increases.

In another embodiment, illustrated schematically in FIG. 5 , genomic DNA 1901 is fragmented with a restriction enzyme, for example, BamHI, which generates a single stranded overhang for sticky ended ligation. The fragments 1905 are ligated to adaptors 2207 that include a label 2205 and a universal priming site 2203. Different adaptors vary in the label portion 2205 but have a common priming site 2203. The label is 3′ of the universal priming site so that it is between the fragment and the universal priming site. The adaptor ligated fragments are amplified by PCR using primer 2209. The PCR product can be fragmented, labeled with a detectable label and hybridized to an array. The resulting strands are detected by hybridization to an array having target-label probes 2210 and includes different features for each target-label combination. The array has a different feature for each target-label-tag combination. The PCR amplicons may be fragmented prior to array hybridization. Preferably the fragments are labeled, for example, by TdT incorporation of a nucleotide that can be detected, such as a biotin containing nucleotide.

The probes of the array are complementary to the junction between the label and the restriction fragment. The sequences at the ends of the individual strands of the restriction fragments are predicted based on in silico digestion of the human genome. Also, fragments are targeted that are within the size range that is known to amplify efficiently by adaptor ligation PCR, for example, 200 bases to 2 kb. The adaptor 2201 had two segments, a constant priming region 2203 and a variable label region 2205. Together 2203 and 2205 form the label adaptor 2207. The primer 2209 has the same sequence 5′ to 3′ as the 2203. The schematic is drawn showing only one strand, but one of skill in the art would understand that in a preferred embodiment the genomic DNA is double stranded and the restriction fragments have two strands, which may be referred to as a top strand and a bottom strand. The convention is that the top strand is drawn 5′ to 3′ left to right and the bottom strand is the complement of the top strand and is drawn 3′ to 5′ left to right. Adaptors are preferably double stranded for at least a portion of the adaptor, they may have single stranded overhangs, for example to have “sticky ends” that facilitate hybridization and ligation to the overhang resulting from restriction digestion. In a preferred aspect, the same adaptor can be ligated to the two ends of a strand of a restriction fragment and may be ligated to one or both strands. The adaptor may be ligated to the ends of the top strand in opposite orientations as shown in FIG. 22 , so that the label is internal to the priming site at both ends. The adaptor may have a top and a bottom strand and the top strand may be ligated to the top strand of the fragment and the bottom strand ligated to the bottom strand of the fragment. The top and bottom strands of the adaptor may be complementary over the entire length, but often have single stranded regions at one end to facilitate sticky ended ligation to an overhang created by a restriction enzyme.

To test this method several adaptors were generated. The test adaptor has PCR002 (SEQ ID No. 1969) as top or sense strand and BamAdaAS (SEQ ID No. 1970) as bottom or antisense strand.

PCR002 5' ATTATGAGCACGACAGACGCCTGATCT (1969)

BamAdaAS 3 AATACTCGTGCTGTCTGCGGACTAGACTAG 5'P (197 0)

The single stranded region on the right is the BamHI single stranded overhang. Te adaptor also has a half Bg1 II site. The “full length-label” adaptor has SEQ ID No. 1972 as top or sense strand and SEQ ID No. 1973 as bottom or antisense strand.

Sense 5' ATTATGAGCACGACAGACGCCTGATCTNNNNNNNNNNNNNN T

AntiSense 3'AATACTCGTGCTGTCTGCGGACTAGANNNNNNNNNNNN NNACTAG

A 5′ phosphate may be added to one or both strands of the adaptor using, for example, T4 polynucleotide kinase. In some aspects a truncated adaptor may be used. An example of such an adaptor is shown in FIG. 7 , the top or sense strand is SEQ ID No. 1974 and the bottom or antisense strand is SEQ ID No. 1975. The portion of the sequence that has a line through it for both SEQ ID NOs. 1974 and 1975 indicates bases missing as compared to SEQ ID NOs. 1972 and 1973 respectively. The N’s in SEQ ID Nos. 1972-1975 indicate a variable sequence in the adaptor that is different for each different label. For example, if there are 1,920 different labels to be used then the N14 represents the 1,920 different labels.

In some aspects it is preferable to use shorter oligos. The full length adaptor in includes 87 bases. The truncated adaptor has 57 bases. Since 2 different oligos must be synthesized for each different label adaptor (e.g. 1,920 labels requires 3,840 different oligos) shorter adaptors are more economical. The separate oligos are preferably annealed together prior to being combined into a pool for ligation to fragments. The primer may be, for example, SEQ ID NO. 1969 or the 5′ 17 bases of SEQ ID No. 1974.

FIG. 24 shows the results of a control experiment where the test adaptor was ligated to fragmented genomic DNA and analyzed on an array having genomic probes. The DNA was subjected to fragmentation with a BamHI, the test adaptor was ligated to the ends and SEQ ID No. 1969 was used as a primer for PCR amplification. The PCR products were fragmented and end labeled using TdT and hybridized to a CNVtype and HG49 arrays. The upper plot is the number of probes (number of different features where each feature corresponds to a different probe sequence) complementary to restriction fragments in the different size bins shown on the X-axis. The sizes and sequences of restriction fragments from a selected genome can be predicted and binned according to size. The probes of the tiling array (probes essentially all non-redundant sequences in the genome) can be assigned to the restriction fragment to which the probe is complementary. Longer fragments will have larger numbers of probes that are complementary to that fragment, simply because the fragment is longer. Restriction fragment size is distributed based on the frequency of the occurrence of the recognition site. Note that the X axis does not increase linearly. While there are more probes that are complementary to fragments in the bins of size greater than 3000, particularly in the bins between 9000 and 30,000, but the intensity in those size bins is less than the intensity of the bins that are about 400 to about 1800. The larger fragments, greater than 9000 bases, for example, do not amplify efficiently with PCR, resulting in lower representation of those large fragments in the hybridization.

In another example, a truncated label adaptor was used (SEQ ID Nos. 1974 and 1975). The adaptor ligated fragments were extended to fill in the ends with polymerase prior to PCR. Hybridization was done in duplicate to either the CNV-type array or HG49 design C. Fragmented DNA and non-fragmented DNA were plotted. The intensity of the DNA that was not fragmented prior to hybridization is less than the intensity of the fragmented DNA. The peak of the intensity for both plots is at a fragment size of about 900 base pairs.

FIG. 11 shows a theoretical modeling of the number of counters predicted to be observed at least once 3201, exactly once 3202 or exactly twice 3203. A non-depleting reservoir of 960 diverse labels was considered. Equation (1) was used to calculate the at least once curve, equation (2) the exactly once curve and equation (3) the exactly twice curve. The error bars indicate one standard deviation from the corresponding mean value.

$\begin{matrix} {E\lbrack k\rbrack = m\left\lbrack {1 - \left( {1 - \frac{1}{m}} \right)^{n}} \right\rbrack} & \text{­­­(1)} \end{matrix}$

$\begin{matrix} \begin{array}{l} {\text{Var}\lbrack k\rbrack =} \\ {m\left\lbrack {1 - \left( {1 - \frac{1}{m}} \right)^{n}} \right\rbrack\left( {1 - \frac{1}{m}} \right)^{n} + m\left( {m - 1} \right)\left\lbrack {\left( {1 - \frac{2}{m}} \right)^{n} - \left( {1 - \frac{1}{m}} \right)^{2n}} \right\rbrack} \end{array} & \text{­­­(2)} \end{matrix}$

FIG. 12 shows counting results for DNA copy number titrations using microarray hybridization in (A) or DNA sequencing in (B). Dilutions (3.62 ng, 1.45 ng, 0.36 ng and 0.036 ng) of a DNA sample isolated from cultured lymphoblasts of a Trisomy 21 male individual were processed for microarray hybridization (left) and DNA sequencing (right). Three chromosome targets were tested and observed numbers of counters (Y-axis) are shown (curve 1201). The number of target molecules for each sample (X-axis) was determined from the amount of DNA used, assuming a single cell corresponds to 10pg. For comparison, the theoretical counter usage rates from the stochastic model equation are also plotted 1202. Numerical values are provided in Table 4.

BamHI cuts the human genome into an estimated 360,679 fragments with a size distribution of 6 bp to 30,020,000 bp. The median size is 5142 bp and the mean is 8320 bp. There are 79,517 fragments in the size range of 150 bp to 2 kb. For testing it may be desirable to choose fragments that meet selected criteria, for example, within a selected size range, select fragments that have more than 1 probe on the HG49m array, exclude fragments that are in known CNV regions, or exclude fragments having a SNP in the first or last 20-30 bases.

The upper panel of FIG. 26 shows the intensities of 1,152 array probes associated with one gene target on chromosome 4, chr4_01s. The data are from the array with 5 ng DNA, i.e., 1000 copies of the tested gene target. The 1,152 probes shown share the same genomic sequence portion, but have different label sequences. Each black dot represents one label sequence. The left 960 dots (on the left side of the red vertical line) correspond to specific labels (i.e., labels used in ligation reaction), and the right 192 dots correspond to non-specific labels (i.e., labels not used in ligation reaction). The probe intensities were plotted in natural log scale on the y-axis. The blue horizontal line is the threshold determined by analysis algorithm (see Materials and Methods), which has a value of 3,800.

The array design for the experiment represented in FIG. 26 is as follows. For each gene target assayed, the array probe consists of all possible combinations of the 960 label sequence and either of the two BamHI genomic fragment ends. An additional 192 label sequences that were not included in the adaptor pool were also tiled to serve as non-specific controls. This tiling strategy enables consistency check on the number of labels used at the paired ends, since each target fragment is ligated to two independent labels (one on either end), and for the same target fragment, the counts on the left and right side should be very similar.

The lower panel shows the histogram of the intensity data corresponding to 960 specific labels. Also shown in the figure are the 2 fitted normal distributions, designated by red and green curves, respectively. The fitted distributions have the mean and standard deviation of 1447 ± 680 and 12186 ± 3580, respectively. The blue vertical line is the threshold, which has the same value as the blue horizontal line shown in the upper panel. Based on such threshold, 501 probes (i.e., labels) were counted as “used”.

FIG. 27 shows the number of times observed for each of the 960 specific labels. Empirically, we did not observe 349 labels in any of the 20 cases. By model, we would expect to observe 643.05 ± 9.96 labels at least once, which means we expect not to observe 307~327 labels. This result shown was obtained by grouping labels used in independent ligation reactions together. To more accurately estimate the frequency of usage of labels, only data from experiments with low concentrations (0.05 ng and 0.5 ng of DNA ligation amount) were considered. Under each concentration, 5 different gene targets independently ligated to labels at both ends. Therefore, a total of 20 independent reactions (2 concentrations x 5 gene targets x 2 ends) were grouped together. Of these reactions, 1,064 labels were observed; some were observed more often than the others, the frequency of usage of labels ranges from 0 to 6.

FIG. 28 shows one example of the replication process of 500 copies of a gene target. In each subplot, copies of target molecules were plotted in the same order. The y-axis is the relative ratio of the number of amplified molecules over the minimal number of amplified molecules in each PCR cycle. Before PCR, all copies are of equal amount, i.e., each copy has one molecule at cycle 0 (subplot (a)). As the PCR process goes on, we start to see differences in the number of amplified molecules corresponding to different copies of target molecules. For example, in cycle 3 (subplot (b)), the ratio between most and least abundant of amplified molecules is 4. Such ratio becomes larger as the number of PCR cycle increases. In cycle 8 and 15, the ratio becomes 26 and 30, in cycles 8 and 15 respectively (see subplots (c) and (d)). This suggests that the differential usage of labels may be observed before PCR is started. Such difference in the amount of molecules associated with different labels will carry on as PCR process goes on.

PCR simulation. We defined n copies of a gene fragment T, each ligated to a single counter randomly selected from an infinite pool of m unique counters to generate a collection of k resulting counter-ligated gene target molecules T* ={tl_(i), i = 1,2, ..., k}. We assumed that each counter-ligated gene target molecule tl_(i) replicates randomly and independently of other target molecules; and that the replication probability p (i.e., amplification efficiency) of different molecules, tl_(i), remains constant throughout the PCR process. For each tl_(i), we denote the number of molecules at PCR cycle c as N^(c) _(i). When c = 0, N⁰ _(i)) is the initial number of tl_(i). The PCR process at cycle c+1 can be modeled as a series of N^(c) _(i) independent trials that determine the replicability of each of the N^(c) _(i) molecules with replication probability p. Let Δ N^(c) _(i) represent the number of molecules replicated at cycle c+1, then the number of molecule tl_(i) after cycle c+1 is

N_(i)^(c + 1) = N_(i)^(c) + ΔN_(i)^(c),

where the probability of Δ N^(c) _(i) is

$\begin{matrix} {p\left( \Delta N_{i}^{c} \middle| N_{i}^{c} \right) = \begin{pmatrix} N_{i}^{c} \\ {\Delta N_{i}^{c}} \end{pmatrix}p^{\Delta N_{i}^{c}}\left( {1 - p} \right)^{N_{i}^{c} - \Delta N_{i}^{c}}} & \text{­­­(2)} \end{matrix}$

We determined the relative abundance of different counter-ligated gene target molecules tl_(i) upon completion of the simulated PCR run for n = 500, 50, or 5, and p = 0.8, 0.7 or 0.6 (Table 5). In each case, we performed 1,000 independent runs to simulate 30 cycles of adaptor PCR, followed by 30 cycles of gene-specific PCR.

TABLE 5 Shows summary statistics drawn from 100 independent simulation runs modeling PCR, ligation at each end of targets is considered Initial copy number N = 5 N = 50 N = 500 Side Left Right Left Right Left Right #of labels observed 5 5 48.61 0.99 48.64 1.09 388.91 6.85 389.27 7.18 Max (1.43 0.19) ^(∗)10^11 (1.43 0.19) ^(∗)10^11 (2.18 0.49) ^(∗)10^10 (2.13 0.47) ^(∗)10^10 (4.52 0.59) ^(∗)10^9 (4.44 0.55) ^(∗)10^9 Min (5.73 2.27) ^(∗)10^10 (5.73 2.27) ^(∗)10^10 (2.35 1.06) ^(∗)10^9 (2.35 1.06) ^(∗)10^9 (1.15 0.49) ^(∗)10^8 (1.23 0.49) ^(∗)10^8 Ratio btw max & min 3.13 2.44 3.13 2.44 14.10 11.41 13.87 13.42 43.42 25.66 44.92 30.04 Mean (1.00 0.16) ^(∗)10^11 (1.00 0.16) ^(∗)10^11 (1.03 0.06) ^(∗)10^10 (1.03 0.06) ^(∗)10^10 (1.27 0.03) ^(∗)10^9 (1.27 0.03) ^(∗)10^9 Standard deviation (3.44 1.02) ^(∗)10^10 (3.44 1.02) ^(∗)10^10 (3.98 0.52) ^(∗)10^9 (3.94 0.54) ^(∗)10^9 (6.75 0.41) ^(∗)10^8 (6.69 0.40) ^(∗)10^8 Coef. of variation 0.36 0.13 0.36 0.13 0.39 0.05 0.38 0.05 0.53 0.03 0.53 0.03

Focusing on the experiments with concentrations of 0.5 and 0.05 ng, (3^(rd) and 4^(th) in each group of 5), which provide the most accurate count of labels, there are 20 different opportunities for a given label to be observed (2 concentrations x 5 amplicons x 2 sides (left or right)). We observed 1,064 labels over the 20 opportunities.

To observe the distortion of the relative abundance of DNA molecules in the reaction resulting from the PCR process, dispersion in the quantitative distribution of PCR amplified DNA molecules was analyzed. A model of the PCR process was generated to understand the dispersion in the distribution of amplified molecules (FIG. 25 , Table 6). A series of 1,000 independent simulation runs were performed to simulate the replication of uniquely labeled target molecules through PCR processes. For each run, we measured the distribution of the final amount of PCR products and quantified the dispersion of distribution using two measures: ratio of the maximal to the minimal amount, and coefficient of variation of final PCR products. This demonstrates that the degree of dispersion increases with the incidence of replicate use of identical counters, which may be in-part responsible for the deviation observed when assaying high target copy numbers. Table 6 lists the ratio and CV for distributions corresponding to different concentrations and replication probabilities (one sided ligation considered).

TABLE 6 replication probability n=5 n= 50 n = 500 Ratio of max to min amount of PCR amplified product p = 0.6 5.69 ± 4.95 26.16 ± 23.78 124.18 ± 88.04 p = 0.7 4.59 ± 8.03 16.22 ± 15.53 71.55 ± 55.13 p = 0.8 2.82 ± 1.51 11.54 ± 9.53 42.24 ± 27.49 Coefficient of p = 0.6 0.48 ± 0.16 0.51 ± 0.06 0.62 ± 0.03 Variation (CV) p = 0.7 0.41 ± 0.14 0.44 ± 0.05 0.57 ± 0.02 p = 0.8 0.34 ± 0.12 0.36 ± 0.05 0.52 0.02

Example 1 of a method for selecting a collection of labels starting with all possible 14 mers (414 or ~268 million possible labels). Step 1: clustering based on the last 7 bases: all sequences with the same last 7 bases are grouped together; within each cluster, randomly pick one sequence, this gives us 11,025 sequences, denoted by set A. Step 2: clustering based on the first 7 bases: all sequences with the same first 7 bases are grouped together; within each cluster, randomly pick one sequence, this gives us 13,377 sequences, denoted by set B. Step 3: get the union set of set A and B, the combined set has 24,073 sequences. Then do clustering based on the middle 6 bases, randomly pick one sequence out of every cluster, this gives us 3,084 sequences, denoted by set C. Step 4: calculate the all-against-all alignment score of set C, which gives us a 3,084 X 3,084 self-similarity score matrix, denoted by S. Step 5: filter based on the score matrix. If an element of the score matrix S(i,j) has a high value, that means, the corresponding

sequences i and j are very similar to each other. Starting from the elements with top self-similarity score, randomly pick one and discard the other; repeat this process until the number of retained sequences < 2000. Until this step, 1,927 sequences were retained.

For the retained 1,927 sequences, an all-against-all complement score was calculated for each. This gave a 1,927 x 1,927 cross complement score matrix. A step similar to step 5 was performed, to avoid labels with maximal cross-complement with other labels. Starting from the pairs with top cross-complement score, one was randomly pick and the other discarded. This process was repeated until the number of retained sequences was 1920. Next the 1920 labels were split into 2 sets, with one set (denoted by set A) consisting of sequences that are maximum different from one-another; and the other set (denoted by set B) consisting of the remaining sequences. The procedure used to split sequences was as follows. Starting from the original 1920 by 1920 similarity score matrix, for each sequence, (1) sum up all its similarity scores with the rest of the sequences in the pool, that is, for each sequence, calculate a total similarity score. (2) Sort the total similarity scores of all sequences and select the sequence with the lowest total score, and move it to set A. (3) Remove the row and column corresponding to the selected sequence, i.e., both the number of rows and columns in the similarity score matrix are reduced by 1. Repeat steps 1-3, until the number of rows and columns in the similarity score matrix reaches 960 or half of the original. The selected sequences belong to set A and the remaining sequences belong to set B.

In another embodiment a collection of labels is selected using the following steps. Starting with all possible 14 mers (4¹⁴ or ~268 million possible labels) eliminate all that do not have 50% GC content. Eliminate those were each nucleotide does not occur at least twice. Eliminate those that have more than two G/C in tandem or more than three A/T in tandem. Eliminate those that contain a selected restriction site. That reduces the original set to ~33 million or 12.43% of the original set. From that set select those that have a Tm within the range of 38.5° C. to 39.5° C. This step results in a set of ~7 million or 2.73% of the original set. Remove those that have regions of self-complementarity. The resulting set in this example was now 521,291. A hierarchical clustering was performed to identify a set that has maximum sequence difference between one-another. The resulting set contained 1,927 labels. Labels were removed if the sequence had a tendency to bind to other labels in the set. This reduced the set to 1,920 labels. A final set of 960 labels was selected from the 1,920 as being maximally different for the “specific” labels and 192 additional counters to tile on the array as “non-specific” controls.

Selection of Targets and design of test array. Regions selected to assay as targets included Chr X, Chr Y, Chr 4 as a reference and Chr 21 for Trisomy. Locations on the chromosomes for assaying were selected to avoid centromeres and telomeres. Fragments were selected based on Bam HI fragments of between about 400 and 600 base pairs. Fragment intensity was checked using HG49 array hybridization. The first and the last 26 nucleotides of the fragments (from and including the Bam HI site) were tiled. Repeats were avoided and GC% was optimized.

The array format was 100/25. Feature size is 5 um. There are 436 x 436 features or 190,096 features. Synthesis was NNPOC, 43 mer probes, 5′ up, no phosphate. The chip name is STCL-test2. The gridding probe used was the same as the HG49. No QC probes were included.

Aside from reducing whole chromosomes into 360,679 smaller molecular weight DNA pieces more suitable for ligation reactions, restriction digestion also serves to reduce the overall sequence complexity of the sample, as only an estimated 79,517 fragments reside in the 150 bp-2 kb size range that is effectively amplified by PCR . To detect and quantify counters that have been selected by the target molecules, the labeled genomic target fragments may be circularized and PCR amplified to prepare for analysis, for example, using microarray hybridization or DNA sequencing. A representative BamHI target fragment was sampled for each of the three test chromosomes. Simultaneous measurements of all three chromosomes serve as an internal control independent of dilution or other systematic errors. A suitable DNA array detector capable of distinguishing the set of counters bound to copies of the target molecules was constructed using photolithography ( S. P. Fodor et al., Science 251, 767 (Feb. 15, 1991).). Each array element for a target to be evaluated consists of a target complementary sequence adjacent to one of the complements to the 960 counter sequences (FIGS. 1 and 2A). For increased specificity, a ligation-readout was performed on the microarray after hybridization to avoid false positive detection of the cross-hybridization of identical targets with different counters. As a means of validation through a secondary measure, samples hybridized to microarrays were subsequently sampled by DNA sequencing (FIGS. 10 and 29 ).

An equation to model the stochastic labeling of target molecules with a small library of 960 counters, and validate our equation model with numerical simulations is disclosed. In the model, the diversity of counters selected by, and ligated to target molecules in the reaction solution (simplified as ‘used’) is dictated by the number of copies of molecules present for each target fragment in the reaction (FIG. 12 ). Under conditions where the size of the counter library is much greater than the number of copies of a given target molecule, the counting efficiency is high, and counting the number of counters used is equivalent to counting the number of copies of the original target molecules (FIG. 16 ). When the number of target copies approaches and exceeds the number of different counters in the reaction, any counter in the library is more likely to be used multiple times (FIG. 15 ). The number of counters used at least once is an important measure because it serves as the basis for drawing yes/no conclusions in our digital readout on microarrays. Under stochastic labeling conditions, we expect that the absolute quantity of single DNA molecules can be accurately determined by proxy counts of labeling events. Indeed, microarray experiments demonstrate a high degree of correlation between the number of copies of target molecules added to the reaction and the number of counters used, as detected on microarrays (FIG. 12 ). In particular, counter usage precisely profiles the number of target molecules under conditions of high counting efficiency. Subtle deviations from the model may represent minor dilution errors in the preparation of the sample. However, within that sample dilution, the relative counter ratios of the three internally built-in markers are highly accurate (FIG. 13 ). FIG. 13 shows comparison of relative copy ratios of the three gene targets tested: ChrX, Chr4 and Chr21 representing genetic material of one, two and three copies per cell. Different dilutions (5 ng, 2 ng, 0.5 ng and 0.05 ng) of a DNA sample isolated from cultured lymphoblasts of a Trisomy 21 male individual were processed for microarray hybridization and DNA sequencing. The calculated number of target molecules (see, Table 4, column 9) was inferred from the number of counters detected on microarrays (A), and was also calculated for the SOLID sequencing data (B). For each sample dilution, the target copy number ratio of each gene target relative to ChrX is shown.

On the other hand, when target copies exceed ~100, detected labeling events appear to indicate fewer than actual molecules in solution (FIG. 12 inset in graph on left). This deviation was reproducible and consistently observed across multiple microarray experiments, and was also observed in the DNA sequencing experiments (FIG. 12 inset in graph on right). Under-counts of expected labeling events may originate from inadequate detection sensitivity of the microarray platform or from other systematic or indeterminate deficiencies in the sample preparation procedure. PCR, for example, is prone to amplification bias ( T. Kanagawa, J Biosci Bioeng 96, 317 (2003) and M. F. Polz, C. M. Cavanaugh, Appl Environ Microbiol 64, 3724 (1998)), which could hinder the comprehensive detection of labeling events that may be genuinely stochastic.

To confirm the microarray results, a digital sequence counting of individual molecules in the DNA samples hybridized to microarrays was used as a means of validation, and to detect the presence of any false negatives that may have escaped microarray detection. Analysis of mapped sequence reads resulted in counts in agreement to the microarray observations. Furthermore, a second, independent sequencing run was repeated with similar findings (Table 3).

An additional feature of digital sequence counting is that unlike the microarray intensity data (FIGS. 22 and 23 ), which offers lower resolution into the measurement of the concentration dispersion of PCR amplified molecules, sequence counting clearly demonstrates significant variation in the representation of amplified targets (FIG. 29 ), This is consistent with the computed PCR model. Overall, detected counters on the microarray and sequencing experiments correlate well, but a small subset of counters appear to be unique to each process (Table 7). The observed number of labels in common between the microarray and the two sets of sequencing experiments are summarized in the table. The number of labels in each category is included. The categories are as follows: A+1+2 for labels detected in each of the 3 experiments, 1+2 for labels detected only in sequencing runs 1 and 2, 1+A for labels detected in sequencing run 1 and by array, and so on for the amounts of DNA shown in column 3.

TABLE 7 DNA sample A+1+2 1+ 2 1+A 2+A 1 2 A Chr4 Left side 0.036 ng 13 0 0 0 0 0 1 0.36 ng 96 3 0 1 2 2 5 1.45 ng 228 13 4 22 6 10 6 3.62 ng 484 23 2 3 4 6 12 Right side 0.036 ng 14 0 0 0 0 0 0 0.36 ng 100 1 0 0 2 2 7 1.45 ng 249 25 2 0 15 33 5 3.62 ng 511 22 2 1 9 23 11 Chr21 Left side 0.036 ng 18 0 2 0 0 0 0 0.36 ng 150 0 2 4 0 7 4 1.45 ng 324 17 8 1 32 16 2 3.62 ng 637 14 10 0 17 14 4 Right side 0.05 ng 18 0 1 1 0 0 0 0.36 ng 144 0 2 2 0 0 9 1.45 ng 330 34 2 3 15 12 6 3.62 ng 615 29 1 7 5 2 4 ChrX Left side 0.036 ng 11 0 0 0 0 0 0 0.36 ng 42 0 0 0 1 3 8 1.45 ng 137 3 1 5 8 5 5 3.62 ng 274 12 0 2 4 12 5 Right side 0.036 ng 10 1 0 0 1 0 0 0.36 ng 43 0 3 0 4 0 2 1.45 ng 127 15 0 0 11 25 6 3.62 ng 298 12 3 3 24 31 2

For the reverse scenario, high numbers of mapped sequence reads were always observed to correlate with high microarray intensities in these examples. No systematic or sequence correlations, or explanations were identified for the counters that are absent from any given sequencing experiment for which the microarray readout demonstrates a strong signal. While obviously underrepresented in some experiments, the same counters are sometimes present in high sequence counts in other experiments, suggesting that they are available for sequencing. PCR was used to resolve these isolated cases of disagreement and demonstrate these were false negatives in the sequencing experiments (Table 3). Despite their presence in the sequencing library, it is unclear why the counters were not observed or were underrepresented in the original sequencing run, and also in the subsequent replicate sequencing run.

Aside from the comparative analysis of absolute and relative counts of the numbers of target molecules and counter labels, additional ways to assess the stochasticity of the labeling process were evaluated. First, if the labeling process is random, the frequency of incorporation of identical counters in independent events across the paired left and right termini of target fragments should closely resemble outcomes from numerical simulation. Observed counts on microarrays do in fact match closely with numbers obtained from computer simulations (Table 4, columns 10-11). Second, if the target molecules are labeled randomly with an equal likelihood of incorporation for any member of the 960 counters in the library, we would expect the number of repeated observations of counters to follow a stochastic nature. For this analysis, we accumulated a total of 1,064 counter observations over several microarray experiments restricted to low target copy numbers. Exclusion of data from high copy targets was necessary to avoid undercounting labeling events from multiple incidences of identical counters attaching individually to numerous target copies. As a further and final demonstration of stochastic labeling, results show that the frequency of label usage follows a pattern consistent with outcomes from numerical simulation.

CONCLUSION

While preferred embodiments of the present invention have been shown and described herein, it will be obvious to those skilled in the art that such embodiments are provided by way of example only. Numerous variations, changes, and substitutions will now occur to those skilled in the art without departing from the invention. It should be understood that various alternatives to the embodiments of the invention described herein may be employed in practicing the invention. It is intended that the following claims define the scope of the invention and that methods and structures within the scope of these claims and their equivalents be covered thereby. All cited references, including patent and non-patent literature, are incorporated herein by reference in their entireties for all purposes and particularly to disclose and describe the methods or materials in connection with which the publications are cited. 

What is claimed is:
 1. A method A method of preparing a sample, comprising: obtaining a plurality of first molecules and a plurality of second molecules, wherein the plurality of first molecules and the plurality of second molecules are generated from occurrences of a first target molecule and occurrences of a second target molecule, respectively, and labels from a set of diverse labels, wherein the set of diverse labels comprises labels with m different label sequences, wherein one or more of the plurality of first molecules and the plurality second molecules comprises an occurrence of the first target molecule or the complementary thereof and an occurrence of the second target molecule or the complementary thereof, respectively, and a label sequence or the complementary thereof from the set of diverse labels, wherein more than 90% of the plurality of first molecules and the plurality of second molecules have a label sequence that is different from the label sequences on the other of the plurality of first molecules and the other of the plurality of second molecules, respectively, wherein n1 and n2 are a number of occurrences of the first target molecule and a number of occurrences the second target molecule, respectively, and wherein the ratio of the greater of n1 and n2 to m is smaller than 0.2.
 2. The method of claim 1, wherein the plurality of first molecules or the plurality of second molecules comprises labels with k different label sequences, wherein n is n₁ or n₂, wherein m and n are related by E(k), wherein $E(k) = m\left\lbrack {1 - \left( {1 - \frac{1}{m}} \right)^{n}} \right\rbrack,$ and wherein E(k) denotes the mean of k.
 3. The method of claim 1, wherein the plurality of first molecules or the plurality of second molecules comprises labels with k different label sequences, wherein n is n₁ or n₂, wherein m and n are related by Var(k), wherein $\begin{array}{l} {Var(k) = m\left\lbrack {1 - \left( {1 - \frac{1}{m}} \right)^{n}} \right\rbrack\left( {1 - \frac{1}{m}} \right)^{n} +} \\ {\left( {m - 1} \right)\left\lbrack {\left( {1 - \frac{2}{m}} \right)^{n} - \left( {1 -} \right)} \right)\left( \left( \frac{1}{m} \right)^{2n} \right\rbrack,} \end{array}$ and wherein Var(k) denotes the variance of k.
 4. The method of claim 1, wherein the plurality of first molecules or the plurality of second molecules comprises labels with t different label sequences exactly x times, wherein n is n₁ or n₂, wherein m and n are related by E(t), wherein $E(t) = \frac{mn!}{x!\left( {n - x} \right)!}\left( \frac{1}{m} \right)^{x}\left( {1 - \frac{1}{m}} \right)^{n - x},$ and wherein E(t) denotes the mean of t.
 5. The method of claim 1, wherein the plurality of first molecules or the plurality of second molecules comprises the labels exactly x times, wherein n is n₁ or n₂, wherein m and n are related by Var(t), wherein $\begin{array}{l} {Var(t) = A\left( {1 - A} \right) + \left( {m - 1} \right)m,\left( \begin{array}{l} n \\ {2x} \end{array} \right),} \\ {\left( \frac{2}{m} \right)^{2x}\left( {1 - \frac{2}{m}} \right)^{n - 2x}\left( \begin{array}{l} {2x} \\ x \end{array} \right)\left( \frac{1}{2} \right)^{2x},} \end{array}$ wherein Var(t) denotes the variance of k, and wherein $A = m\begin{pmatrix} n \\ x \end{pmatrix},\left( \frac{1}{m} \right)^{x}\left( {1 - \frac{1}{m}} \right)^{n - x}.$ .
 6. The method of claim 1, wherein the ratio of the greater of n₁ and n₂ to m is smaller than 0.02.
 7. The method of claim 1, comprising detecting the plurality of first molecules and the plurality of second molecules by detecting the label sequences present on the plurality of first molecules and the plurality of second molecules or products thereof, wherein the detected first molecules and the detected second molecules indicate the number of occurrences of the first target molecule and the number of occurrence of the second target molecule, respectively.
 8. The method of claim 7, wherein detecting the label sequences present on plurality of first molecules comprises obtaining sequences of the plurality of first molecules.
 9. The method of claim 8, wherein obtaining the sequences present on the plurality of first molecules comprises sequencing the plurality of first molecules or products thereof.
 10. The method of claim 9, further comprising mapping sequencing reads that are obtained from sequencing the plurality of first molecules, or products thereof, to a reference sequence.
 11. The method of claim 9, further comprising aligning sequencing reads obtained from sequencing the plurality of first molecules, or products thereof.
 12. The method of claim 9, further comprising detecting a mismatch in the label sequence or the copy of the first target molecule in sequencing reads obtained from sequencing the plurality of first molecules, or products thereof.
 13. The method of claim 9, wherein sequencing the plurality of first molecules comprises sequencing a portion of the label sequence or a portion of the copy of the first target molecule, or a product thereof.
 14. The method of claim 9, wherein the label sequences present on the plurality of first molecules indicates the number of occurrences of the first target molecule.
 15. The method of claim 14, comprising scoring a label sequence in sequencing reads obtained from sequencing the plurality of first molecules or products thereof.
 16. The method of claim 7, wherein the detecting step comprises detecting the label sequences present on amplification products of the plurality of first molecules and the plurality of second molecules.
 17. The method of claim 16, wherein the amplification products comprise polymerase chain reaction (PCR) amplification products.
 18. The method of claim 16, further comprising performing one or more amplification steps to generate the amplification products.
 19. The method of claim 1, wherein the copy of the label sequence of a first molecule of the plurality of first molecules is 3′ to the copy of the first target molecule of the first molecule.
 20. The method of claim 1, wherein the copy of the label sequence of a first molecule of the plurality of first molecules is 5′ to the copy of the first target molecule of the first molecule.
 21. The method of claim 1, wherein the obtaining step comprises generating the plurality of first molecules and the plurality of second molecules from the occurrences of the first target molecule and the occurrences of the second target molecule, respectively, and labels from the set of diverse labels.
 22. The method of claim 21, wherein the generating step comprises reverse transcription of an occurrence of the first target molecule and/or the second target molecule.
 23. The method of claim 21, wherein the generating step is performed using a reverse transcriptase, a polymerase, or a combination thereof.
 24. The method of claim 1, wherein the copy of the first molecule in a first molecule of the plurality of first molecules comprises a reverse complement of the first molecule, or a portion thereof, and wherein the copy of the label sequence in the first molecule of the plurality of first molecules comprises a reverse complement of a label sequence of a label of the set of diverse labels.
 25. The method of claim 1, wherein the copy of the first molecule in a first molecule of the plurality of first molecules comprises a reverse complement of the first molecule, or a portion thereof, and wherein the copy of the label sequence in the first molecule of the plurality of first molecules comprises a label of the set of diverse labels, or a portion thereof.
 26. The method of claim 1, wherein the first target molecule comprises an oligonucleotide.
 27. The method of claim 26, wherein the oligonucleotide is ribonucleic acid (RNA) or deoxyribonucleic acid (DNA).
 28. The method of claim 1, wherein the first target molecule comprises RNA, and wherein the second target molecule comprises DNA.
 29. The method of claim 1, wherein one or more of the first target molecule and the second target molecule comprise a RNA, DNA, antibody, or a combination thereof.
 30. The method of claim 1, wherein the first target molecule is associated with an antibody. 31-38. (canceled) 